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CIGRÉ Canada Conference on Power Systems Montreal, Oct. 1-4 2006
Extracting Features for Power System Vulnerability Assessment from Wide-Area Measurements
Innocent Kamwa (IREQ), Ashok Pradhan, Géza Joós (McGill University) CANADA
.
[email protected]
SUMMARY Using wide-area measurement data different features are extracted for post-contingency vulnerability assessment of a power system. Both time and frequency domain features are obtained for wide range of system conditions of a 67-bus power system. The damping parameters are estimated through Prony analysis using the filtered signals. Clustering technique is applied to the features obtained which is another step in possible applications for situational awareness. Results for the power system are demonstrated for the different techniques applied.
KEYWORDS Wide-area measurements, phasor measurement units, power system stability, online system monitoring, dynamic security assessment, vulnerability assessment
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1. INTRODUCTION With deregulation power systems are being forced to operate closer to their stability limits and are more vulnerable following a contingency. Utilities have been installing phasor measurement units (PMUs) to monitor dynamics of the power system. The synchronized phasors of different areas available through a wide-area measurement system (WAMS) are expected to provide an effective security assessment tool, a stabilizing control action for interarea oscillations and a system protection scheme (SPS) to evade possible blackouts in a power system [1]-[6]. Recently, US House of Congress has mandated in its Energy Act for real-time monitoring of interconnections which could provide near-instant picture of transmission system health, early warning for deteriorating system condition, wide-area system visibility, improved transmission reliability planning, and superior diagnostic tools [7]. All these requirements demand for proper analysis of the volume of data accumulated through WAMS which is intricate. Tools extracting features for vulnerability assessment from WAMS-data are proposed in this paper which will be beneficial to operation and planning at an energy management centre. Most of the work related to vulnerability assessment is framed using simulated data or local information, like techniques for first swing stability using time domain approach, direct stability estimation or hybrid methods [8]. To estimate the damping and frequency of inter area oscillations Prony analysis is applied using time domain data, as an off-line tool [9]-[10]. For voltage stability issues, different indices are proposed using local bus voltage information only [11]. All these techniques may not be suitable for vulnerability assessment with data obtained through WAMS. Using WAMS-data a Fourier transform based technique is proposed for monitoring inter area oscillations [11]. FFT, wavelet transform and curve fitting approaches are tried in [12] to analyze oscillatory signals with such data. With wide area measurement, a dynamic voltage stability prediction algorithm is proposed for possible control action [6]. In the present paper an integrated framework has been proposed to assess the system, through extracted features from wide-area measurements, on first swing stability, voltage stability and inter area oscillations. The centre of inertia (COI) concept is applied in this work to angle of voltage phasor and product of frequency and angle difference termed as dot product signal is used in the analysis. Such signals are processed through low pass filter banks to estimate the spectral density which relates to system energy during disturbance. To the filtered signals Prony analysis is applied to extract the damping coefficients and this combined approach provides accurate estimation of damping parameters. For voltage stability issues the minimum postfault voltage of an area is taken into consideration and an algorithm monitoring these indicates the status regarding voltage stability issues. Data clustering technique is applied to classify the features into a certain group for better system visualization. The overall performance of the approach is studied on a 67-bus system with 38 PMUs. The paper is organized as follows. Section II describes on the test power system. In section III the method to extract features both from frequency and time domain analysis is provided. To demonstrate the performance of the approach Section IV provides sample results on the test system followed by conclusion in section V. 2. SYSTEM DESCRIPTION The power system considered is shown in Fig.1 which has 67 buses, 23 machines, 7 GW of nonlinear loads spread over nine electrically coherent areas [2]. For the system optimum number of PMUs has to be fixed locating in different areas. For this, measurement units are first placed at the boundaries of different areas. Then a sequential addition algorithm is applied to include more number of PMUs and simultaneously observing the amount of 3
incremental information acquired by the new PMU. In this process when the entropy based criterion for the incremental information finds a small change the addition process stops. This process provides minimum number of PMUs and when applied to the 67-bus system 38 PMUs locations are obtained [3]. Fig.2 provides the details about the positions of PMUs in different areas. Voltage phasors are sampled at these locations at a varying rate of 1 point to 6 points per cycle at fault inception and data are captured up to 600 cycles after the fault. Area-1
Area-2
5 PMUs(9-bus) MW-614/415 MVAR-216/115
5 PMUs(9-bus) MW-278/415 MVAR-167/115
H -11.9 s
H-4.86 s
Area-5
Area-3
Area-4
4 PMUs(9-bus) MW-345/360 MVAR-178/115
5 PMUs(9-bus) MW-363/315 MVAR-151/115
4 PMUs(9-bus) MW-278/295 MVAR-106/115
H -7.08 s
H -7.54 s
H -7.63 s
Area-7
Area-6
Area-9
Area-8
4 PMUs(5-bus)
4 PMUs(6-bus) MW-1400/1567 MVAR-547/100 H -26.3 s
3 PMUs(5-bus) MW-1400/967 MVAR-408/100
3 PMUs(6-bus) MW-1419/1767 MVAR-361/100 H -23.9 s
MW-1419/1167
MVAR-178/115 H -24.7 s
Fig.1. The test power system
H -22.3 s
Fig. 2.PMU arrangement in different areas
3. FEATURES FOR VULNERABILITY ASSESSMENT In the proposed method the PMU signals are segregated area-wise so that the features obtained can also indicate about the vulnerable area. For vulnerability assessment the magnitude of the voltage phasor is observed through time with specific criteria. The angle information of each area is first transformed on sample to sample basis to obtain a set of resourceful signal for disturbance characterization. To such signals filtering technique is applied to estimate energy information of a disturbance. For estimating damping coefficients Prony analysis is performed to the filtered signals. Broadly the followed process, as shown in Fig.3, provides both frequency and time domain features for power system vulnerability following a contingency. Energy based criteria
PMU1
PMUi
PMUN
Area-wise data separation
Signal
Transformation with centre of inertia concept
Filter banks Prony analysis for oscillatory phenomenon
Voltage criteria
Fig.3. Block diagram showing steps for the proposed feature extraction approach For extracting purposeful features from PMU-information, selection of proper signals is important. The signals considered include PMU data; voltage phasor magnitude and angle of all areas of the system and the signals are transformed suitably for providing meaningful information to the vulnerability assessment process. Assuming each area to be coherently following a disturbance the centre of inertia (COI) concept is applied to the angle of voltage phasor. The derived signals for different areas using COI concept are obtained as follows. For each area k an average angle is found out from measurements through Nk PMUs in that area.
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θ (t ) =
1 Nk
Nk
∑θ (t )
(1)
i
i =1
where θi is the angle measurement through ith PMU in the area. For r areas in a system, the COI signal is defined as
θCOI (t ) =
1 MT
r
∑θ (t )
(2)
j
j =1
where MT is the total inertia of the power system, defined as, r
MT = ∑ M i
(3)
j =1
The COI signal thus obtained is used to derive resourceful signals which are being used in the feature extraction process. The derived angle signal for ith area becomes
θi (t ) = θi (t ) − θCOI (t ) coi
(4) and corresponding frequency of the i area, th
ωicoi (t ) = θi coi (t )
(5) Composed from the above two signals the dot product signal ( x ) for ith area is defined as, xi (t ) = ωicoi (t )[θi coi (t ) − θ i (0+ )] (6)
x1 (n) x2 (n)
xr (n)
X 1 (k )
max
X 2 (k ) max
X 1m X 2m
max
peak of the spectral density ( X im ) is computed area wise and then the overall peak is computed for the system. This is shown in Fig.4 where n and k represent for time and frequency respectively. With the input data window shifting sample by sample the corresponding time varying frequency domain index related to kinetic energy injected into the system following contingency can be obtained for the most disturbed area in the system.
Filter bank- Based PSD Estimator
Where θi (0+ ) corresponds to the value immediately at the clearing instant. The dot product signal is further processed both in frequency and time domain to extract features for assessment purpose. 3.1 Frequency domain features It is understood that the spectral density of oscillatory signals relates to kinetic energy injected to the system during fault. The power spectral density (PSD) obtained through filter bank approach is used in this work. The dot-product signals are resampled at a fixed rate (20 Hz in this case) and a data window of each area is fed to the filter bank designed specifically to capture the oscillatory phenomenon. The
Xm
X r (k ) max X rm
Fig.4 PSD estimation through filter banks
The filters used for the PSD estimation have frequency response as shown in Fig.5 where first 8 channels are used for the purpose. This indicates that each area filtered signal ( X i ( k ) ) consists of 8 band filtered signals and X im is the peak value of all such 8 signals in ith area at that instant.
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(a) sampling rate Fs=20Hz (b) sampling rate Fs= 60 Hz Fig. 5 Frequency response of the first eight channels of filter-banks 3.2 Time domain features (a) Voltage criteria
Most of the stability challenges are related to voltage issues. To the voltage magnitude as obtained for different areas a voltage stability criteria is set. In this processing, the considered signal of an area at each instant is the minimum voltage of all measurements of that area. In the voltage context, the minimum voltage of the system with a 2 s and 5 s sliding windows after the clearance of the fault (Vcriterion(2s) and Vcriterion(5s) respectively) are good indicative of system condition which are used as features in this approach. (b) The COI angle difference The COI angle deviation with respect to prefault value is computed for each area and the maximum value of such differences is found to be a good measure of the topological stress induced by the contingency. coi coi PostFltDTH= max (θi prefault − θi (t )) (7) i=1:r
( c) Damping Analysis
Inter area oscillation threats almost all power systems at times which is difficult to access. Wide-area phasor measurements seem to be promising mechanism to provide valuable information on estimating the dominant electro-mechanical oscillatory modes of the system. FFT, wavelet transform and curve fitting approaches are tried in [12] to analyze oscillatory signals with PMU data. Using Fourier spectrum a method to estimate the eigenvalue is proposed [11] which needs an averaging technique and the accuracy is a concern. Prony analysis is used with simulated data for extracting frequency and damping coefficients [9]-[10]. Such analysis performs poorly when a signal is embedded in noise. In this work the band selective filtered signal as obtained for dot product signal is used. This integrated approach overcomes the noise problem and enhances the accuracy of the method. When the PSD and associated voltage will clearly indicate about the system passing through a multi-swing unstable period, modal analysis is not a necessary. For other situations the Prony analysis is applied to suitable filtered signals. The first 6 channel signals of all areas (6rsignals) are considered and for each channel the signal with maximum strength is selected (refer Fig.). Prony analysis estimates the parameters by fitting a sum of complex damped sinusoids evenly sampled in time. The detailed analysis process is available in [9]. The damping coefficient as defined in this paper is obtained with the following formula-
ξ =−
α
(8)
α 2 + ω2 Where α and ω are rate and frequency terms of a damped sinusoid. 4. RESULTS The 67-bus test system was studied earlier also] for wide area severity index (WASI) based study for dynamic security assessment [2. It is possible to collect extensive sets of data for vulnerability assessment of the system using wide area measurement data concept. For the
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study 480 cases have been selected which covers wide range of phenomenon related to stability of the system following contingencies. To illustrate the performance of the techniques proposed few cases are discussed with the results. Subsequently a clustering based automatic classification strategy and corresponding results using the features are presented. 4.1 Case-1 - Fig.6 provides the result for a case where the first plot refers to COI angle of all 9 areas after the clearance of a fault and computed using the relation (4). This plot shows that after the disturbance all areas oscillate with respect to each other with varying degree and after a period of 20 s the oscillations die down. The PostFltangle calculated using relation (7) is -3.32 deg, a small value. As inferred this is clearly a stable case. Plot 2 in the figure is the slow WASI based frequency domain feature as obtained from the filter banks with dotproduct signal. The plot with on a log scale indicates the effect of the disturbance on different area related to kinetic energy injected to the system. The thick dotted line in this plot is for the SlowWASI feature index for the case. The corresponding feature value SlowWASI (5s) is -2.5519 indicating the associated energy to be comparatively low. Similarly the third plot on a log scale is obtained applying the filter of Fig.5(b) to dot product signals of 9 areas and the resultant FastWASI feature index is plotted with thick dotted line. This plot also indicates about a comparatively low kinetic energy injected and a dying characteristic. The corresponding FastWASI (2s) is -4.537 a low value for this stable case. The fourth plot refers to minimum voltage of each area which relates to the time domain feature where the thick dotted line refers to that for VCriterion(5s) feature index. The voltage of the disturbance originating area oscillates more but finally all such voltage stabilises. The corresponding VCriterion(2s), VCriterion(5s) and PostEventVoltage are 0.906 p.u, 0.991 p.u. and 0.991 p.u. respectively indicating that for a stable system. PostFltAngle=−3.3283 Deg
COI−Angle(deg.)
R1 R2
5
R3 R4
0
R5 R6 R7
−5 0
5
10
15
20
R8 R9
25
Slow WASI
SlowWASI(5s)=−2.5519;PostEventWASI=−7.2476 −3
−4
−5
0
5
10
15
20
25
Fast WASI
FastWASI(2s)=−4.537; FastWASI(1s)=−4.3842
−6 −8 −10
0
5
10
15
20
25
Area Voltage(pu)
PostEventV=0.99151p.u. VCriterion(5s)= 0.99147 p.u.; VCriterion(2s)=0.90688p.u.
1.02 1 0.98 0
5 10 15 20 Time [s]−−−CaseName:wasi.dsaIK97_cc_9_8_test0ik06
25
Fig. 6 Case-1 A secure state following a contingency 7
The damping analysis is carried out as it is a relatively stable case as inferred from energy and voltage features in the observed period of 25 s. As mentioned the Prony analysis uses first 6channel of the filter; selecting only one signal for each channel corresponding to the area signal with largest magnitude in that channel (refer Fig.4 ). In this case channel-2 has highest peak among the filtered signals. Applying the Prony method to this signal the dominant 0.06
Amp Freq( Hz)
0.04
0.042 1.580 0.181
ξ
0.022 1.979 0.045
oscillating frequency components are identified which are provided inside the plot of Fig.7. The estimated signal by the method matches closely to the actual signal as observed in the figure which indicates on the accuracy of the approach. Similar results are obtained for other 5 channel signals. The positive damping for all observable modes and corresponding low amplitudes and the earlier features indicate that in the observed period the system is relatively stable.
0.017 0.876 0.256
0.02
X2r 0
-0.02
-0.04
-0.06
5
10
15
20
Time(s)
Fig.7. Modal analysis of case-1,
25
actual ------ estimated
4.2 Case-2 In a similar way to previous case four plots for case-2 are provided in Fig. 8. The COI- angle plot indicates a growing oscillation in area 6 which ultimately results in a system collapse after 16 s of the disturbance. The post fault angle difference is significantly high in this case (-19.58 deg). The slow WASI plots show high energy inflow to many of the areas with high SlowWASI (5s) and FastWASI(2s) indices as provided in table-1. The growing voltage deterioration (starting in area 6) and ultimately resulting voltage collapse is also noticed from voltage plot. This is clearly an unstable case. PostFltAngle=−19.5878 Deg
COI−Angle(deg.)
R1 R2
0
R3 R4
−200
R5 R6 R7
−400 0
2
4
6
8
10
12
14
16
R8 R9
SlowWASI(5s)=2.4165;PostEventWASI=2.5446
Slow WASI
2 0 −2 −4 0
2
4
6
8
10
12
14
16
FastWASI(2s)=0.060233; FastWASI(1s)=−0.52217
Fast WASI
0
−5
−10
0
2
4
6
8
10
12
14
16
Area Voltage(pu)
PostEventV=0.69082p.u. VCriterion(5s)= 0.88746 p.u.; VCriterion(2s)=0.77973p.u.
1 0.8 0.6 0
2 4 6 8 10 12 14 16 Time [s]−−−CaseName:wasi.testIK97_test6ik97_test0ik06
Fig.8. Case-2 An insecure state following a contingency
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4.3 Case-3 The angle plot in Fig. 9 shows that the system is yet to be stabilized after the 25 s of the disturbance clearance though the oscillations are within limits (see case-1). The slowWASI plot shows medium level of peak (between the earlier two cases) and similar inference is observed with fastWASI. The voltage plot shows that area-2 has initial jerk in voltage but with time all voltages are within limit. As observed from the data in table 1 the system is stable in the voltage sense also. PostFltAngle=−9.3475 Deg
COI−Angle(deg.)
R1 R2
20
R3
10
R4 R5
0
R6
−10
R7
0
5
10
15
20
R8 R9
25
Slow WASI
SlowWASI(5s)=−0.24199;PostEventWASI=−1.6598 −1 −2 −3 −4 −5
0
5
10
15
20
25
FastWASI(2s)=−2.6531; FastWASI(1s)=−1.806 −2
Fast WASI
−4 −6 −8 −10
0
5
10
15
20
25
Area Voltage(pu)
PostEventV=0.97684p.u. VCriterion(5s)= 0.94824 p.u.; VCriterion(2s)=0.79279p.u.
1 0.95 0.9 0.85 0
5 10 15 20 Time [s]−−−CaseName:wasi.testIK97_dsa2ik97_test0degrad1ik06
25
Fig. 9 Case-3, A secure case with a large topological stress 0.6
Amp Freq( Hz)
0.4
ξ
0.459 1.087 0.426
0.391 0.841 0.206
0.288 1.653 0.083
0.086 2.150 0.150
Prony estimates for channel-2 signal which has maximum peak in the observed period is provided in Fig.10 which contains also the details of the 4 dominant frequencies of the signal. The all positive damping coefficients (with relatively larger amplitudes) and the features of high energy inflow and low Vcriterion(2s) indicate that the system was in stress initially but could able to sustain the contingency in the observed period of 25 s.
0.2
X2r
0
-0.2
-0.4
-0.6
-0.8
5
10
15
Time(s)
Fig. 10 Modal analysis of case-3,
20
25
actual ------ estimated
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4.4 Case-4 The first plot on COI angles in Fig. 11 for this case indicates that the system is heading towards an uncontrollable situation. The slow and fast WASI plots also show relatively high energy input during the disturbance. The fourth plot shows that the voltage degrades rapidly beyond 20 s and it is clearly a case of voltage instability. Further as indicated in table 1 the indices for this case though relatively of less energy associated than case-2 the voltage indices clearly indicates about the system situation. PostFltAngle=−10.6173 Deg
COI−Angle(deg.)
R1
50
R2 R3 R4
0
R5 R6
−50
R7
0
5
10
15
20
R8 R9
25
SlowWASI(5s)=1.0741;PostEventWASI=1.6152
Slow WASI
0 −2 −4 0
5
10
15
20
25
FastWASI(2s)=−1.5991; FastWASI(1s)=−1.6331
Fast WASI
−2 −4 −6 −8 −10
0
5
10
15
20
25
Area Voltage(pu)
PostEventV=0.81532p.u. VCriterion(5s)= 0.92456 p.u.; VCriterion(2s)=0.74246p.u.
1 0.9 0.8 0
5 10 15 20 Time [s]−−−CaseName:wasi.testIK97_dsa1ik97_test0degrad1ik06
25
Fig. 11 Case-4, An insecure case of voltage instability Table 1 Obtained features for different cases Features
Case-1
Case-2
Case-3
Case-4
SlowWASI(5s)
-2.55
2.41
-0.84
1.07
FastWASI(2s)
-4.53
0.06
-2.65
-1.59
PostEventWASI
-7.24
2.54
-1.43
1.61
PostFltAngle_diff
3.32
19.58
8.01
10.61
VCriterion5s
0.99
0.88
0.95
0.92
VCriterion2s
0.90
0.77
0.82
0.74
PostEventV
0.99
0.69
0.97
0.81
Definitions used for the features in table-1 are summarized as below. 1. SlowWASI(5s) = long-window based system-wide WASI, sampled value at 5s after fault clearing [Log(deg.Hz)] 2. FastWASI(2s) = short-window based system-wide WASI, sampled value at 2s after fault clearing[Log(deg.Hz)] 3. PostEventWASI= end value of long-window based system-wide WASI [Log(deg.Hz)] 4. PostFltAngle_diff = system-wide maximum difference between the pre-fault and post-fault COI-angle (deg.) 5. VCriterion5s = system-wide minimum voltage over a 5-s sliding window, sampled value at 5s after fault clearing (pu) 6. VCriterion2s = system-wide minimum voltage over a 2-s sliding window, sampled value at 2-s after fault clearing(pu) 7. PostEventV = end value of system-wide minimum voltage over a 2-s sliding window (pu)
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4.4 Clustering Approach Applying clustering strategy to the features 1.000 2.000 as more usable resources for possible applications, two clusters are performed based on features from COI signals and voltage signals. In the first clustering three feature indices are considered; (i) postfault_DTH (ii) slowWASI (5s) and (iii) fastWASI(2s) and in voltage based approach three indices are taken into account; (i) postevent voltage (ii) VCriterion2s and (iii) VCriterion5s. The k-means clustering technique is applied to all 480 cases selected 3.000 4.000 for the study. (a) Using COI signals As shown in Fig.12 the technique divides the cases into 4 classes (class 1-4). These classes indicate about the status of the system, for example, class-1 possess lower values of all indices comparatively (low energy disturbance) indicating a stable don’t_care situations. On the other hand Fig.12.Clustering study of 480 cases with 4 classes using three angle features class-4 is a high_alert situation. COI_class
(b)Using voltage signals In a similar way to earlier clustering, considering only voltage based features 4 classes are obtained and shown in Fig. 13. The 4 clusters are representative of different status of the system as regard to voltage strength, for example class-1 here indicates about a stable don’t_care situation as all indices are close to 1.0 p.u. The four cases demonstrated in earlier section are applied through the clustering process for classification. The results are provided in table-2. For case-1, relatively a secure case as discussed earlier, the COI_class is 1 and volt_class is 3. Case-2 an insecure situation is refereed to COI_class 4 and volt_class 2.
1.000
2.000
3.000
4.000
Fig.13. Clustering study of 480 cases with 4 classes using three voltage features, volt_class
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Table-2 Classification results with clustering approach Class-Type Classification result Case-1 Case-2 Case-3 Case-4 COI_class 1 4 3 3 Volt_class 3 2 1 2 5. CONCLUSIONS Applying wide-area measurement concept different features are extracted for postcontingency vulnerability assessment of a power system. Damping analysis is also carried out using the filtered signals and clustering technique is applied to the different features for purposeful vulnerability classification. Results for the power system indicate that such a strategy will be beneficial for operators at an EMS centre. 6. BIBLIOGRAPHY [1]
[2] [3] [4] [5] [6] [7]
[8] [9] [10] [11] [12] [13]
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