RECENT developments have seen lot of power system

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1 Auto Detection of Power System Events Using Wide Area Frequency Measurements Gopal Gajjar and S. A. Soman Dept. of Electrical Engineering, Indian Institute of Technology Bombay, India and Abstract The wide area frequency measurement system has been installed at several locations in power system. There are plans to install phasor measurements units (PMU) at almost all high voltage substations. The volume of data obtained from such systems is very large. While most of the time the power system is in ambient condition, however there are always several events per day occurring in the system. This paper presents a method to automatically detect such events from wide area frequency measurement data. The PMUs measure bus voltage frequency communicate them to a central location in real time at rate of one sample per power system cycle. These measurements are be fed to the auto event detection algorithm. The method of detection of event occurrence identification, event classification and exact instance of event occurrence identification is presented. The issues encountered in implementing such scheme is discussed in the paper. Index Terms WAMS applications, Power Swings, Auto Event Detection, Principal Component Analysis, Chi Square Distribution, Kalman Filter I. INTRODUCTION RECENT developments have seen lot of power system measurements being collected at central locations in real time. The measurements can include bus voltage and transmission line current phasors, the bus frequency and rate of change of frequency. The rate of measurements is in the range of one sample per cycle or one sample per two cycles. While the power system is in quasi steady state at almost all the time only perturbed by small variations in load and generation. However there are also few events daily like major faults or disconnections of a large load or generators. The power system operators keep constant vigil on the system health through monitoring the measured values and the output of the online tools like state estimators, static and dynamic security assessment. This model of power system operation is suitable for the data measurement through polling of remote terminal units. Any events like fault or tripping of load or generators is conveyed through binary signals and the final effect of the event on the system is perceived by the operators after the runs of state estimators and security assessment tools. The time taken in this process could range in terms of few minutes. With PMU measurements, binary data as well as the response of the system to the event is quickly communicated to the system control centers. In some cases when an event occurs outside the observable region the binary signal may not be communicated, still its effect can be observed on the phasor measurements. With automatic identification of events from PMU measurements the operators can be alerted earlier about the occurrence of the event as well as its severity and impact on the power system. The auto event detection can also be used to trigger a run for dynamic security assessment (DSA) thus giving a more detailed system assessment as soon as the system configuration is altered due to major event. Thus having automatic event identification can be useful for better system situation awareness. There are applications like event based power system oscillation mode identification using frequency data. These applications use the PMU measurements of frequency to identify the oscillation frequency, damping factor, phase difference and magnitude of oscillations. The system security can be assessed through computation of the frequency and damping factor of the post fault electromechanical oscillations. While severity and the type of the event can be judged through the magnitude of the oscillations. The accuracy, consistency and reliability of these methods is dependent on the exact identification of beginning of the event. Automatic event detection algorithm should also identify the beginning of the event and the duration of the oscillations to be considered for the input of the oscillation mode identification application. This paper presents a method for automatic event identification using the wide area frequency measurement data. The following sections give background about power system oscillations, present the method for event detection and method for identifying exact event instant and duration. Few cases studies are given later to highlight the effectiveness of method and discuss the implementation issues encountered. II. ELLIPSOID METHOD Methods of identifying the power system events using frequency measurements appear easy until they are applied and tested on real life data. Here we have adopted a statistical method called method of ellipsoids for auto detection. This method has been employed for similar purpose [1]. We have extended the method reliably identify the events other than loss of load or generation. Here we briefly describe the method and the extensions. Let Y a and Y b be two time series having frequency measurement data from two different locations a and b. Hence,

2 Y a = [y a (1), y a (2),, y a (n)] T (1) Y b = [y b (1), y b (2),, y b (n)] T (2) With n numbers of synchronized samples. Similarly any numbers of data vectors can be defined. Defining Y cov R 2x2 as sample covariance matrix between Y a and Y b. Y cov (1, 1) = 1 Y cov (1, 2) = 1 Y cov (2, 1) = 1 Y cov (2, 2) = 1 y a (k) Ỹa y a (k) Ỹa (4a) y a (k) Ỹa y b (k) Ỹb (4b) y a (k) Ỹa y b (k) Ỹb (4c) y b (k) Ỹb y b (k) Ỹb (4d) Where Ỹa and Ỹb are the sample mean values of samples Y a and Y b respectively. If a n m data matrix Y is formed as, [ ] Y = Y a Ỹa, Y b Ỹb,, Y m Ỹm (5) then Y cov can be express compactly as, Y cov = 1 YT Y (6) A. Principal Component Analysis Principal Component Analysis (PCA) is applied on this covariance matrix to get the decoupled orthogonal vector space for variances of the two frequency measurements. PCA transforms data to a new set of variables called Principal Components (PCs), which are uncorrelated and which are ordered in descending order of variance [2]. It is defined as linear combinations of the column of data matrix that maximizes the variance of the combined vector. Hence it can be written as, { [ max var α T Y ]} st. α T α = 1 (7) where α R m is the first PC. var [ α T Y ] can also be expressed as α T Y cov α. It can be shown that solution of (7) is same as the eigen vector α 1 of Y corresponding to its largest eigen value. The maximum eigen value λ 1 is the variance of the transformed variable. Similarly it can be also shown that the eigen vectors and eigen values in the descending orders give the transformation vectors and the corresponding variance of the next highest variance among the data vectors. The transformed variables can be calculated as n m transformed matrix X from A as set of orthogonal eigen vectors of Y cov. X Scatter of Frequency of and Mean of Frequencies X 1 Fig. 1. Frequency and Scatter Plot. A = [α 1, α 2,, α m ] (8) X = Y A (9) Fig. 1 explains the concept of PCA through an example. Fig. 1a shows synchronized frequency measurement at two locations and for duration of 1 s, sampled at uniform period of 2 ms. This two dimension data can be also viewed as a scatter plot Fig. 1b. The scatter plot between the two transformed variables X 1 and X 2 is shown in Fig. 1c. In this case X 1 represent the variable with largest variance equal to the largest eigen value λ 1 of Y cov, and X 2 represent the variance of the second eigen value λ 2 in this case it is also the smallest eigen value. Ideally when the power system is in steady state or with disturbed with a small random load and generation variation, the frequency measured at two locations does not vary too much from each other. This is reflected in the scatter plot with variance along X 1 being much larger than that along X 2. The variation along X 1 represent the random variance in the system frequency due to system wide load and generation imbalance. The variation along X 2 represent the difference in frequencies at the two locations that can be due to measurement errors and the random load and generation variation at each location. The variances can be quantified and used for detecting power system events. B. Error The load and generation variations either system wide of at each location can be considered as normally distributed

3 X X Scatter of Frequency of and Mean of Frequencies Fig. 2. Scatter and. random processes. Distribution of the sum of squares of k independent random variables with normal standard distribution is known as χ 2 -distribution with k degrees of freedom. For general normally distributed random processes with variance not equal to 1, the variance can be normalized if the two processes are uncorrelated. It can be shown that the Cumulative Distribution Function (CDF) of χ 2 -distribution with m degree of freedom is related to ellipsoid defined by, ρ 2 = Y T Y cov 1 Y (1) such that CDF(ρ) of χ 2 -distribution with m degrees of freedom percentile of points in a scatter plot with m variables lie inside the ellipsoid with ρ radius measured in Mahalanobis Distance (MD) [3], [4]. (1) can be equivalently written as, where, ρ 2 = Y T Λ 1 Y (11) Λ = diag [λ 1, λ 2,, λ m ] For a two dimensional ellipsoid with radius ρ = 1.6, 99.5 percentile points will lie inside because CDF(1.6) is.995 with χ 2 -distribution with 2 degrees of freedom. For the data used in Fig. 1 the ellipsoid with ρ = 1.6 is shown in Fig. 2a. The transformed ellipsoid in actual frequencies is shown in Fig.2b. III. COARSE EVENT DETECTION Any large power system will have a few dominant electromechanical modes of oscillations that observable in most of the system measured values. The bus voltage frequency is one of such output variable. The modes of oscillations can be broadly classified as inter area, local and intra plant modes. It is known that the a large power system event like a short circuit fault on a line or a bus, tripping of a generator or large load shedding due to operation of some protection devices will cause power system electromechanical oscillations. Each of these events have their own signature response that can be observed in the frequency measurements. X X 1 Fig. 3. A. Detection of small events Event1 - Sensitivity for small event detection. We device ways to detect such events in power system using the method of PCA and error ellipsoid. The power system events can be small or big depending on the type of faults and post fault scenarios. They are accordingly reflected in frequency as a big or small excursions. The basic method to detect an event is to apply a threshold on the magnitude of the error variance in the transformed variables. Consider Fig. 3. It shows a small event that is due to a fault in a 22 kv line cleared by opening of the line through primary protection. It gives rise to a frequency excursion that has a duration of about 5 s. This is typical of any fault event in the system. The event detection works in blocks of 5 s data on which PCA is employed and the error ellipsoid is made. The length of the minor axis of the ellipsoid depends on the variance λ 2 of the second transformed variable X 2. When there is no event its value is below some threshold. If the length of the minor axis of error ellipsoid is greater than a threshold value an power system event is detected. L minor axis > (12) The threshold value depends on the ambient conditions and the normal variance in the frequency measurement systems. In our system it was decided through observations of many events and long duration ambient measurements. The selected threshold is given in (12), and Fig. 3c demonstrate the event detection using this threshold. This is the smallest event that can be detected using this threshold.

4 X X Pre Fault Mean Pre Fault Fault Mean Fault Fig. 4. Event2 - Detection of Major Event. Fig. 5. Event3 - Detection of generation tripping event. B. Detection of major events In case of a fault in a major transmission line carrying heavy power the frequency excursions can be quite large. Moreover the major events can be also caused due to delayed tripping or sequential clearing of the faults. It can involve more than single tripping of lines and buses. Because of these reasons the even in a well damped system the duration of frequency excursion can be quite long. To detect such events we perform the PCA and error ellipsoid methods for frequency samples of duration of 5 s, 1 s and 2 s. The threshold of event detection is kept same as in (12). However, in case of a small fault just the 5 s batch detects event while for major fault all the three batches are triggered. This distinguishes the major events and minor events. One drawback of this method of detection of major events is that although the event is detected, but as we use a long duration of 2 s frequency data, the method cannot pin point the exact instance of occurrence of event. This method give a coarse duration with range of 2 s the event could have occurred any time within that period. Fig.4 shows a major event. It can be observed that its error variance is well beyond our selected threshold even for the observation duration of 2 s. At same time the event actually occurs at the 6 th s within the data window. C. Detection of load or generation tripping In case of tripping of load or generation it observed the frequency of the whole system changes in the post fault conditions. Traditional methods use some thresholds to detect under and over frequency, however a more sensitive and more reliable method is demonstrated in [1]. We use similar method to detect load and generation tripping. To adopt the method to Indian conditions where frequency variations are more it was found suitable to use longer sample windows for pre fault and fault duration. We use duration of 1 s for pre fault condition and 2 s duration for fault condition. The method calculates error ellipsoid and the Mahalanobis distance of the ellipsoid contour from the mean of the frequency in scatter plot during the pre fault condition. The mean of the frequency in scatter plot for the fault condition is also calculated. The mean of the frequencies represent the centers of their corresponding error ellipsoids. The event is detected in case the center of fault error ellipsoid lie outside the error ellipsoid of the pre fault condition. In other words if the Mahalanobis distance between two centers is greater than 1.6 then a generation or load tripping event is detected. The generator and load tripping are distinguished from each other by comparing the post event frequency to the pre event frequency. Fig. 5 shows detection of a generation trip event. In this case a generation of 3 MW got tripped in the synchronous system having about 6 MW generation. It should be noted that even in this case the exact instance of event occurrence is not detected. IV. IDENTIFICATION OF EVENT INSTANCE Precise identification of instance of occurrence of event is important. One of the main use of auto event detection from frequency measurements is to estimate the system oscillation modes and damping factors. There are several methods of oscillation frequency mode identification like Prony s method [5], Matrix Pencil [6], TLS-ESPRIT [7], [8] etc. Most of these

5 methods model oscillations as linear combinations of damped exponential. Their results are reliable when the actual signal supplied to the method matches this model of damped exponential. Moreover the amplitude of the oscillations estimated by the methods depend on the initial peak values of the input signal. Hence it is necessary that the input signal use for oscillation mode identification is sampled at correct instance and have correct duration. If the signal contains some portion of pre event frequency then the oscillation mode identification methods may show out put with underdamped components. If signal sample is taken a few seconds after the event then signal to noise ratio suffers. Such samples also result into wrong amplitude estimation. Hence, in automated system it is important to get correct instance of event accurate within few ms. The event instance identification can be based on measuring rate of change of frequency (df/dt) in post event scenario. It is recognised that df/dt is very sensitive to any events and variation in it can be used. But before using df/dt based methods some per processing on the signal is required. We use Kalman method to filter the signal to get reliable estimation of df/dt. A. Kalman Filter for df/dt estimation During small system disturbances due to random load and generation variations the power system behaves as a linear time invariant system. We have a continuous observation of the frequency of system which combined with the linear system model can be used to get estimate of the rate of change of frequency. The standard Kalman filter method for this purpose is described in [9], [1]. In discrete linear system we can write x[n + 1] = A d x[n] + w[n] (13) y[n] = C d x[n] + v[n] (14) Where, x = [f df/dt] T is state vector with frequency f and rate of change of frequency df/dt as two states. w is vector of disturbance with normal distribution, zero mean and a known covariance matrix. v is measurement noise vector with normal distribution, zero mean and a known covariance. v is uncorrelated with w. A d is state transition matrix and C d is observation matrix with structure, A d = [ ] 1 T 1 (15) C d = [1 ] (16) A d represent frequency as integration of df/dt with T equal to the sampling time. Standard Kalman filter is applied to (15) with following Raw measurements FIR filtered Kalman Filtered Df/dt FIR filtered Df/dt Kalman filtered Fig. 6. parameters Performance of Kalman Filter in estimation of df/dt. [ ] 1 P = 1 [ ].1 Q = 1. (17) (18) R = [.1] (19) T =.2 (2) (21) Where, P is initial error covariance matrix, Q is estimate of covariance matrix of w and R is estimate of covariance matrix of v. The performance of the filter with parameters is shown in Fig.6. The raw measurements of frequency is first filtered with an FIR filter to remove high frequency noise, this is than supplied to the Kalman filter. Fig.6b shows comparison of df/dt estimated through output of just FIR filter through differencing and the df/dt estimated through Kalman filter. It can be observed that there are spikes in df/dt estimated by FIR filter while Kalman filter gives smooth df/dt. The spikes are caused by missing data and bad samples which are common occurrence in any practical measurement systems. It must be noted that both frequency and df/dt plots are intentionally offset with some amount for better representation in graph. In actual data all graph overlap with each other. B. Event instance identification The event instance is identified through variance of the df/dt. A sample by sample moving window variance of df/dt signal with window length of 1 s is calculated. In ambient conditions the variance of the df/dt signal is close to zero, the small value of variance during ambient condition is due to noise in df/dt. While during any event the variance changes significantly. A threshold technique is applied to detect the beginning of the event. The threshold is decided with keeping sensitivity in mind. We can afford to be sensitive in this case as we have

6 Df/dt (Hz/s) Df/dt (Hz/s) df/dt Kalman Filtered df/dt Kalman Filtered Event df/dt Kalman Filtered Event Fig. 7. variance of df/dt Df/dt measured for the three events. Event variance of df/dt Event at s Event at s Event variance of df/dt Event at 16.4 s Event Fig. 8. Detection of event instance. Event3 remove the noise in df/dt and made it smooth through Kalman filter, moreover the event instance identification is applied to only small window of data around which the occurrence of event is already identified by error ellipsoid method. Hence possibility of false detection is very small. The threshold is taken as maximum of.5 or 1% of the peak value of the variance measured in the sample. Fig. 7 shows the df/dt measured for the three events previously discussed. Fig. 8 shows the event instance identification through threshold method. The results of event instances are mentioned in the Fig. 8, it can be observed that the event instances are identified accurately in all the three cases. V. CONCLUSIONS This paper demonstrate methods for auto identification of power system events through frequency measurements. During this exercise it is experienced that the reliable event identification is non trivial task in automated fashion, with the performance criteria such that there are no false detection and at same time ensuring all events are correctly identified and classified. Both minor events and major events pose different problems in correct identifications. Finally not just event identification but the instance of event detection is also a challenging task in real life measuring systems with missing and outlier samples. A reliable yet sensitive system for event instance identification is devised here. A version of this system is kept in automated mode to continuously monitor system frequency in Indian power system through Wide Area Frequency Monitoring Systems. ACKNOWLEDGMENT The authors would like to thank Prof. A M Kulkarni and his students for creating the Wide Area Frequency Measurement System and providing the data collected through it for this research. REFERENCES [1] R. M. Gardner and Y. Liu, Generation-load mismatch detection and analysis, IEEE Transactions on Smart Grid, vol. 3, no. 1, pp , Mar [2] I. T. Jolliffe, Principal Component Analysis, ser. Springer Series in Statistics. New York: Springer-Verlag, 22. [3] G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, Time Series Analysis: Forecasting and Control. Hoboken, NJ: John Wiley & Sons, Inc., Jun. 28. [4] L. Mili, M. Cheniae, N. Vichare, and P. Rousseeuw, Robust state estimation based on projection statistics [of power systems], IEEE Transactions on Power Systems, vol. 11, no. 2, pp , May [5] J. Pierre, D. Trudnowski, and M. Donnelly, Initial results in electromechanical mode identification from ambient data, IEEE Transactions on Power Systems, vol. 12, no. 3, pp , Aug [6] J. Quintero, G. Liu, and V. M. Venkatasubramanian, An oscillation monitoring system for real-time detection of small-signal instability in large electric power systems, in Power Engineering Society General Meeting. IEEE, Jun. 27, pp [7] P. Tripathy, S. C. Srivastava, and S. N. Singh, A modified TLS-ESPRIT- Based method for Low-Frequency mode identification in power systems utilizing synchrophasor measurements, IEEE Transactions on Power Systems, vol. 26, no. 2, pp , May 211. [8] G. R. Gajjar and S. A. Soman, Power system oscillation modes identifications: Guidelines for applying TLS-ESPRIT method, in 17th National Power System Conference, Varanasi, Dec [9] Q. Zhao, J. Dong, T. Xia, and Y. Liu, Detection of the start of frequency excursions in wide-area measurements, in Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 28 IEEE. IEEE, Jul. 28, pp [1] A. Girgis and T. Daniel Hwang, Optimal estimation of voltage phasors and frequency deviation using linear and non-linear kalman filtering: Theory and limitations, IEEE Transactions on Power Apparatus and Systems, vol. PAS-13, no. 1, pp , Oct