PMU-based Voltage Instability Detection through Linear Regression

Transcription

1 PMU-based Voltage Instability Detection through Linear Regression Rujiroj Leelaruji and Prof. Luigi Vanfretti Smart Transmission Systems Lab. Electric Power Systems Department KTH Royal Institute of Technology, Sweden Second Rio International Workshop on Synchrophasor Applications Universidade Federal do Rio de Janeiro / COPPE December 4, 2013

2 Acknowledgement The work presented in this presentation is funded by the European Commission through the FP7 itesla Project. The support from the EC is gratefully acknowledged.

3 Outline Goals of the study Differences with previous work Methodology - Linear Regression method for estimating sensitivities from PMU measurements Simulation Results - Real-Time Hardware-in-the-Loop Setup - Test results from real-time simulation model - Application to Real PMU data from the Norwegian Grid

4 Concept A two layer approach for Defense Plans using PMU Data and Controls Stable Threshold Unstable Current operating point identified by PMU WAMS Approaches to prevent a voltage instability in defense mode mode: Activate an specific control mode (e.g. HVDC, SVC) using a defense signal obtained from sensitivities computed from PMU data. Coordinate with internal controls: for example Reduce Power Order of HVDC when surpass MTP-Point, change the set point of SVC.

5 Methodology: Detection Voltage Sensitivities Real-Time Simulator PMU (V and I Phasors at each line) Filtering Sensitivity Computation Reconstruction of individual components of sensitivities (for each transmission line) Real-Time Hardware-in-the-Loop Simulation Extraction of short-term dynamics and errors Comparison with Thresholds Visualization Derivation of Wide-Area Early Warning Signals Wide Area Display and Alarming

6 Methodology: Defense PMU Data Filtering and Data Conditioning Load Shedding Yes Current operating point identified by PMU WAMS Early-warning Computation of Sensitivities No > Final Warning threshold Stable Final No > Early Warning threshold Activate SVC Activate SVC DEFENSE Controls DEFENSE Controls Yes Identify problematic location Selection of control feedback input signals Unstable

7 Main Goals of this Study: Computation of Sensitivities This study focused on the following aspects: - A simple method sensitivity computation: Reduce difficulties related to filtering techniques for preprocessing data. Use only the measurements to reconstruct individual sensitivities. Fast and accurate computation technique suitable for real-time applications. - How to compute sensitivities from actual PMU data considering: Fast dynamics, and measurement features (outliers, errors, etc. in PMU data). How to treat the behavior of actual measured PMU data (compared to typical positive sequence simulations that are commonly used). Differentiate process noise versus measurement noise produced by PMUs. - How to use sensitivities to derive: Wide-Area Early Warning Signals using sensitivities

8 Differences with Previous Work Previous work from Glavic and Van Cutsem focused on sensitivity computation using a model linked to PMU measurements. Main differences with Glavic and Van Cutsem s approach: - We assume full PMU coverage: All voltage and current phasors at every line are measured - We have NO knowledge of the power network No model individual of sensitivities are reconstructed from measurements - Short-term dynamics EMTP-type model running with PMU in real-time hardware-in-the-loop simulation: OEL, LTC (at each phase) and load dynamics are included. As well as PMU data outliers and errors, which are extracted previous to computing sensitivities Hence the sensitivities are NOT derived from a model but instead measurements are used to reconstruct them - Generator control and limits are modeled in full detail However their actual control mode (voltage control or limitation) is not known by the methodology THIS CAN BE DETECTED from the change in computed sensitivities Other work by Mani V. focuses in reconstructing the whole of each power flow sensitivity (considering all injections to the bus) from measurements OVER a long time span - Here all line voltages and current phasors are available, hence - We compute each individual sensitivities independently, for each line - We do this for a very short time span and thus the method has real-time computation constraints

9 Methodology: Detection Real-Time Simulator PMU (V and I Phasors at each line) Real-Time Hardware-in-the-Loop Simulation Linear Regression Extraction of short-term dynamics and PMU errors Sensitivity Computation Reconstruction of individual components of sensitivities (for each transmission line)

10 NO Linear Regression Method for the Estimation of Sensitivities from PMU Data Synchonized Voltage & Current Phasors P i -P i-1 < k m *ε m Q i -Q i-1 < k n *ε n Step 1 Step 2 Step 3 Step 5 YES Calculate Active & Reactive power Update with incoming raw data NO Determine linear correlations of voltage and powers Step 4 Good-of-fitness R 2 volt< 0.3 & t > t window Reduce window size YES Slope i = Slope i Slope i = Slope i-1 YES Step 6 Compute sensitivites New data NO END

11 Linear Regression (cont.) Methodology: Linear Regression (LR) - Inputs: voltage & current phasors at buses with PMU. - Outputs: V i P ik and Vi Q ik sensitivities. - How this method works: Step 1: Gather voltage & current phasors from every available bus with PMU. Step 2: Calculate active and reactive powers from the gathered votlage and current phasors from following equations:

12 Linear Regression (cont.) Step 3: Find the linear correlation of measured voltage and calculated powers: Vm ti Vm ti t i-1 t i

13 Linear Regression (cont.) Step 4: Check the quality-of-fitness Calculate Coefficient of determination (R 2 ) where Total sum of square: Total sum of square residuals: The value of R 2 lies between [0, 1]. R 2 = 0 indicates no linear relationship.

14 Voltage (p.u.) Voltage (p.u.) Linear Regression (cont.) Thus, the window size should be reduced to increase R 2 value. Not too big Look at linear behaviour of physical system Voltage Magnitude Too big window size: R 2 1 ok window size: R 2 1 Zoom Time(sec.) But it should not be too small computation issue Voltage Magnitude Too small window size ok window size Time(sec.)

15 Linear Regression (cont.) Step 5: Update incoming raw data. Step 5.1: Replace the oldest measured data by the newest data as shown below (where the window size is unchanged). N-window size Step 5.2: Check the development of loads. if loads remain unchange; where k is sensitivity factor. Step 6: Calculate sensitivities The sensitivity can be calculated; Similar expression goes to the sensitivity.

16 Real-Time Hardware in the Loop Simulation Experiment Set-Up Real-Time Simulator (Model running in RT) PDC receiving phasors Amplifiers interfacing relays PMUs/Relays computing phasors and sending out to network

17 SEL-421 Relay with PMU functionality GPS Antenna GPS Signals Spliter Monitoring Output Measurement (3-Phase signals) Three-Phase Voltage & Current Signals GPS Antenna Input Ethernet Port Data Stream on IEEE C Opal-RT OP5600 Computational Target Analog Outputs from IO to Megger SMRT1 Megger SMRT1 (Back Panel) Megger SMRT1 (Front Panel)

18 Test System model for real-time simulation Steam Turbine Speed-governor Overexcitation Limiter Test System Other components OLTC Transformer Random load variation (process-noise)

19 Modeling for Real-Time Hardware in the Loop Simulation Generate 3-Phase RT Signals (Voltages and Currents) 3-phase voltage 3-phase current OLTC discrete(!) operations occur at each phase, at different time instants!

20 ` ` ` ` Simulations results Test System Tr1 L1 Tr2 OLTC Gen /230 L / Test Cases Scenarios Case 1: Only OLTC activation 1. Without random load variation Case 2: Only OEL activation 2. With random load variation Case 3: OTLC & OEL activation

21 Simulations results (cont.) Scenario 1: Without random load variation (process noise), HIL simulation (measurement noise included) window size = 2 sec, k= , ε= *Load is increased at time = 50 sec

22 Simulations results (cont.) Scenario 1: Without random load variation (process noise), HIL simulation (measurement noise included) Zoom Activation of system components can be detected by checking R 2 of measured voltage

23 Simulations results (cont.) Scenario 1: Without random load variation (process noise), HIL simulation (measurement noise included) V 5 P 45

24 Simulations results (cont.) Scenario 2: With random load variation (process noise), HIL simulation (measurement noise included) Case 3 SNR = 10 Process Noise Active power Voltage Voltage - zoom

25 R 2 of measured voltage Simulations results (cont.) Scenario 2: With random load variation, HIL simulation (measurement noise included) Case 3 SNR = Inf & 10 Process Noise OLTC Activation OEL Activation Time(sec.) R 2 of measured voltage Without Noise With Noise

26 dvdp (p.u.) Simulations results (cont.) Scenario 2: With random load variation, HIL simulation (measurement noise included) Case 3 Different levels of process noise 4 3 SNR = inf, k = SNR = 50, k = SNR = 10, k = Time(sec.) V 5 P 45

27 dvdp (p.u.) Simulations results (cont.) Comparison with and without process noise 4 3 Case 1 Case 2 Case 3 OEL Activation Without noise Time(sec.) With noise

28 Real PMU Data from the Norwegian Grid PMU locations

29 Determining Thresholds through the Analysis of Atypical Events Base-lining Study in large network. 12 PMUs in substations in the Norwegian power system 3 days (72 hours) of data Many many signals!

30 Base-lining Study (cont.) Example: Hourly voltage deviation Upper limit (defined) Ascertain daily profiles Lower limit (defined)

31 Base-lining Study (cont.) 3-days deviation More extreme cases More deviation

32 Wide-Area Early Warning Signals using sensitivities voltage dvdq

33 Conclusions and Further Work Conclusions Fast and simple sensitivities calculation. Voltage instability Early Warning Signal and Final Alarming. Further work Close-loop control for preventing voltage instability.

34 Thank you! Acknowledgement to