A generalized subspace least mean square method is presented for accurate and robust estimation of oscillation modes from exponentially damped power system signals. The method is based on the orthogonality of signal and noise eigenvectors of the signal autocorrelation matrix. Performance of the proposed method is evaluated using Monte Carlo simulation and compared with the Prony method. Test results show that the generalized subspace least mean square method is highly resilient to noise and significantly dominates the Prony method in tracking power system modes under noisy environments.

%B Electric Power Components and Systems %V 41 %P 1205 - 1212 %8 09/2013 %N 12 %! Electric Power Components and Systems %R 10.1080/15325008.2013.807896 %0 Journal Article %J IEEE Transactions on Power Systems %D 2013 %T Mode shape estimation algorithms under ambient conditions: A comparative review %A Luke Dosiek %A Ning Zhou %A John W. Pierre %A Zhenyu Huang %A Dan Trudnowski %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K phasor measurement units (PMUs) %K power systems %X This paper provides a comparative review of five existing ambient electromechanical mode shape estimation algorithms, i.e., the Transfer Function (TF), Spectral, Frequency Domain Decomposition (FDD), Channel Matching, and Subspace Methods. It is also shown that the TF Method is a general approach to estimating mode shape and that the Spectral, FDD, and Channel Matching Methods are actually special cases of it. Additionally, some of the variations of the Subspace Method are reviewed and the Numerical algorithm for Subspace State Space System IDentification (N4SID) is implemented. The five algorithms are then compared using data simulated from a 17-machine model of the Western Electricity Coordinating Council (WECC) under ambient conditions with both low and high damping, as well as during the case where ambient data is disrupted by an oscillatory ringdown. The performance of the algorithms is compared using the statistics from Monte Carlo simulations and results from measured WECC data, and a discussion of the practical issues surrounding their implementation, including cases where power system probing is an option, is provided. The paper concludes with some recommendations as to the appropriate use of the various techniques. %B IEEE Transactions on Power Systems %V 28 %P 779 - 787 %8 05/2013 %N 2 %! IEEE Trans. Power Syst. %R 10.1109/TPWRS.2012.2210570 %0 Journal Article %J IEEE Transactions on Power Systems %D 2012 %T A Stepwise Regression Method for Estimating Dominant Electromechanical Modes %A Ning Zhou %A John W. Pierre %A Dan Trudnowski %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K phasor measurement units (PMUs) %K Power system stability %K RTGRM %X Prony analysis has been applied to estimate inter-area oscillation modes using phasor measurement unit (PMU) measurements. To suppress noise and signal offset effects, a high-order Prony model usually is used to over-fit the data. As such, some trivial modes are intentionally added to improve the estimation accuracy of the dominant modes. Therefore, to reduce the rate of false alarms, it is important to distinguish between the dominant modes that reflect the dynamic features of a power system and the trivial modes that are artificially introduced to improve the estimation accuracy. In this paper, a stepwise-regression method is applied to automatically identify the dominant modes from Prony analysis. A Monte Carlo method is applied to evaluate the performance of the proposed method using data obtained from simulations. Field-measured PMU data are used to verify the applicability of the proposed method. A comparison of results obtained using the proposed approach with results from a traditional energy-sorting method shows the improved performance of the proposed method. %B IEEE Transactions on Power Systems %V 27 %P 1051 - 1059 %8 05/2012 %N 2 %! IEEE Trans. Power Syst. %R 10.1109/TPWRS.2011.2172004 %0 Conference Paper %B 2011 North American Power Symposium (NAPS 2011) %D 2011 %T Evaluation of mode estimation accuracy for small-signal stability analysis %A Jim Follum %A Ning Zhou %A John W. Pierre %K AA09-002 %K AARD %K Automatic Switchable Network (ASN) %K load modeling %K power system monitoring %X This paper proposes a method for determining electromechanical mode estimate accuracy by relating mode estimate error to residual values. Mode frequency and damping ratio were estimated using Prony analysis and residuals were calculated for a 17-machine model with varying levels of load noise. Mode estimate error and residuals were found to increase proportionally to each other as noise values were increased, revealing a distinctly linear relationship. The use of these results to develop appropriate confidence in models is discussed. With the relationship established, a method of predicting mode estimate error values based on residuals in the western North American power system (wNAPS) was developed. The potential of this method to evaluate the confidence level of mode estimates is examined. %B 2011 North American Power Symposium (NAPS 2011) %I IEEE %C Boston, MA, USA %P 1 - 7 %8 08/2011 %@ 978-1-4577-0417-8 %R 10.1109/NAPS.2011.6024893 %0 Conference Paper %B IEEE Power and Energy Society (PES) General Meeting %D 2011 %T The influence of topology changes on inter-area oscillation modes and mode shapes %A Yousu Chen %A Jason C. Fuller %A Ruisheng Diao %A Ning Zhou %A Zhenyu Huang %A Francis K. Tuffner %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K damping %K power grid operations %K Power system stability %K WECC %XThe topology of a power grid network is a piece of critical information for power grid operations. Different power grid topologies can change grid characteristics, inter-area oscillation modes, mode shapes, and even the robustness of the power system. This paper presents some preliminary study results, based on an approved WECC operating case and a modified low damping WECC system, to show the impact of topology changes resulting from N-1 contingencies on power system modes and mode shapes. The results show that topology changes can have very different impact on modal properties in a power system: some result in an unstable situation, while others can improve small signal stability. For the former, the studies show about a 4.5% damping reduction, so a 5% damping margin would be required to ensure the system can sustain the contingencies. For the latter, those topology changes could be used as a control method to improve small signal stability. Mode shapes normally do not change when there is an N-1 topology change. These observations suggest that the inclusion of topological information is useful for improving the accuracy and effectiveness of power system control schemes.

%B IEEE Power and Energy Society (PES) General Meeting %I IEEE %C Detroit, MI, USA %P 1 - 7 %8 07/2011 %@ 978-1-4577-1000-1 %R 10.1109/PES.2011.6039904 %0 Conference Paper %B IEEE Power and Energy Society (PES) General Meeting %D 2011 %T A modified stepwise linear regression method for estimating modal sensitivity %A Ning Zhou %A Zhenyu Huang %A Francis K. Tuffner %A Dan Trudnowski %A William A. Mittelstadt %K AA09-002 %K AARD %K Automatic Switchable Network (ASN) %K phasor measurement units (PMUs) %K power system reliability %XSmall signal stability problems are one of the major threats to grid stability and reliability. Low damping of inter area modes is usually considered to be a result of heavy power transfer over long distances. This paper proposes a modified stepwise regression method to estimate the modal sensitivity with respect to power flow on the transmission lines based on measurement. This sensitivity is used to identify dominant transmission lines, whose power flow has significant influence on the inter-area modal damping. It is shown through simulation study that the proposed method can effectively estimate the modal sensitivity with respect to line power flow. This, in turn, provides insight on how to improve damping through adjusting tie line flow.

%B IEEE Power and Energy Society (PES) General Meeting %I IEEE %C Detroit, MI, USA %P 1 - 7 %8 07/2011 %@ 978-1-4577-1000-1 %R 10.1109/PES.2011.6039795 %0 Conference Paper %B 2011 44th Hawaii International Conference on System Sciences (HICSS) %D 2011 %T Use of Modal Sensitivity to Operating Conditions for Damping Control in Power Systems %A Zhenyu Huang %A Ning Zhou %A Francis K. Tuffner %A Dan Trudnowski %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K damping %K oscillations %K power system control %K Power system dynamics %K Power system stability %XSmall signal stability is an inherent characteristic of dynamic systems such as power systems. Pole positioning through power system stabilizers (PSS) is often used for improving damping in power systems. A well-designed PSS can be very effective in damping oscillations, especially local oscillations. However, designing PSSs for inter-area oscillations has been a very challenging task due to time-varying operating conditions affecting the oscillations. This paper explores the sensitivity relationship between oscillations and operating conditions, and employs the relationship to derive recommendations for operator's actions to adjust operating conditions for improving damping. Low damping is usually considered to be a result of heavy power transfer in long distance, while specific locations also have significant impact on damping of oscillations. Therefore, it is important to consider locations in deriving recommendations. This paper proposes the concept of relative modal sensitivity and presents its application in deriving recommendations for operator's action in damping control.

%B 2011 44th Hawaii International Conference on System Sciences (HICSS) %I IEEE %C Kauai, HI %P 1 - 9 %8 01/2011 %@ 978-1-4244-9618-1 %R 10.1109/HICSS.2011.469 %0 Conference Paper %B IEEE Power and Energy Society (PES) General Meeting %D 2010 %T Automatic implementation of Prony analysis for electromechanical mode identification from phasor measurements %A Ning Zhou %A Zhenyu Huang %A Francis K. Tuffner %A John W. Pierre %A Shuangshuang Jin %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K grid reliability %K phasor measurement units (PMUs) %K power system monitoring %XSmall signal stability problems are one of the major threats to grid stability and reliability. Prony analysis has been successfully applied on ringdown data to monitor electromechanical modes of a power system using phasor measurement unit (PMU) data. To facilitate an on-line application of mode estimation, this paper develops a recursive algorithm for implementing Prony analysis and propose an oscillation detection method to detect ringdown data in real time. By automatically detecting ringdown data, the proposed method helps to guarantee that Prony analysis is properly and timely applied on the ringdown data. Thus, the mode estimation results can be performed reliably and timely. The proposed method is tested using Monte Carlo simulations based on a 17-machine model and is shown to be able to properly identify the oscillation data for on-line application of Prony analysis.

%B IEEE Power and Energy Society (PES) General Meeting %I IEEE %C Minneapolis, MN %P 1 - 8 %8 07/2010 %@ 978-1-4244-6549-1 %R 10.1109/PES.2010.5590169 %0 Conference Paper %B IEEE PES General Meeting %D 2010 %T Improving small signal stability through operating point adjustment %A Zhenyu Huang %A Ning Zhou %A Francis K. Tuffner %A Yousu Chen %A Dan Trudnowski %A William A. Mittelstadt %A John F. Hauer %A Jeffery E. Dagle %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K phasor measurement units (PMUs) %K Power system stability %X ModeMeter techniques for real-time small-signal stability monitoring continue to mature, and more and more phasor measurements are available in power systems. It has come to the stage to bring modal information into real-time power system operation. This paper proposes to establish a procedure for Modal Analysis for Grid Operations (MANGO). Complementary to PSS and other traditional modulation-based control, MANGO aims to provide suggestions such as redispatching generation for operators to mitigate low-frequency oscillations. Load would normally not be reduced except as a last resort. Different from modulation-based control, the MANGO procedure proactively maintains adequate damping at all times, rather than reacting to disturbances when they occur. The effect of operating points on small-signal stability is presented in this paper. Implementation with existing operating procedures is discussed. Several approaches for modal sensitivity estimation are investigated to associate modal damping and operating parameters. The effectiveness of the MANGO procedure is confirmed through simulation studies of several test systems. %B IEEE PES General Meeting %I IEEE %C Minneapolis, MN %P 1 - 8 %8 07/2010 %@ 978-1-4244-6549-1 %R 10.1109/PES.2010.5589519 %0 Conference Paper %B IEEE Power and Energy Society (PES) Transmission and Distribution Conference %D 2010 %T Initial studies on actionable control for improving small signal stability in interconnected power systems %A Francis K. Tuffner %A Zhenyu Huang %A Ning Zhou %A Ross T. Guttromson %A Jayantilal, Avnaesh %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K Power system modeling %XPower consumption and demand continues to grow around the world. As the electric power grid continues to be put under more stress, the conditions of instability are more likely to occur. One cause of such instabilities is intearea oscillations, such as the oscillation that resulted in the August 10, 1996 blackout of the WECC. This paper explores different potential operations of different devices on the power system to improve the damping of these interarea oscillations using two different simulation models.

%B IEEE Power and Energy Society (PES) Transmission and Distribution Conference %I IEEE %C New Orleans, LA, USA %P 1 - 6 %8 04/2010 %@ 978-1-4244-6546-0 %R 10.1109/TDC.2010.5484340 %0 Journal Article %J IEEE Transactions on Power Systems %D 2010 %T Probing Signal Design for Power System Identification %A John W. Pierre %A Ning Zhou %A Francis K. Tuffner %A John F. Hauer %A Dan Trudnowski %A William A. Mittelstadt %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K WECC %X This paper investigates the design of effective input signals for low-level probing of power systems. In 2005, 2006, and 2008 the Western Electricity Coordinating Council (WECC) conducted four large-scale system-wide tests of the western interconnected power system where probing signals were injected by modulating the control signal at the Celilo end of the Pacific DC intertie. A major objective of these tests is the accurate estimation of the inter-area electromechanical modes. A key aspect of any such test is the design of an effective probing signal that leads to measured outputs rich in information about the modes. This paper specifically studies low-level probing signal design for power-system identification. The paper describes the design methodology and the advantages of this new probing signal which was successfully applied during these tests. This probing input is a multi-sine signal with its frequency content focused in the range of the inter-area modes. The period of the signal is over 2 min providing high-frequency resolution. Up to 15 cycles of the signal are injected resulting in a processing gain of 15. The resulting system response is studied in the time and frequency domains. Because of the new probing signal characteristics, these results show significant improvement in the output SNR compared to previous tests. %B IEEE Transactions on Power Systems %V 25 %P 835 - 843 %8 05/2010 %N 2 %! IEEE Trans. Power Syst. %R 10.1109/TPWRS.2009.2033801 %0 Conference Paper %B 2009 IEEE Power & Energy Society General Meeting %D 2009 %T Electromechanical mode shape estimation based on transfer function identification using PMU measurements %A Ning Zhou %A Zhenyu Huang %A Luke Dosiek %A Dan Trudnowski %A John W. Pierre %K AA07-001 %K AARD %K Automatic Switchable Network (ASN) %K phasor measurement units (PMUs) %K Power system modeling %X Power system mode shapes are a key indication of how dynamic components participate in low-frequency oscillations. Traditionally, mode shapes are calculated from a linearized dynamic model. For large-scale power systems, obtaining accurate dynamic models is very difficult. Therefore, measurement-based mode shape estimation methods have certain advantages, especially for the application of real-time small signal stability monitoring. In this paper, a measurement-based mode shape identification method is proposed. The general relationship between transfer function (TF) and mode shape is derived. As an example, a least square (LS) method is implemented to estimate mode shape using an autoregressive exogenous (ARX) model. The performance of the proposed method is evaluated by Monte-Carlo studies using simulation data from a 17-machine model. The results indicate the validity of the proposed method in estimating mode shapes with reasonably good accuracy. %B 2009 IEEE Power & Energy Society General Meeting %I IEEE %C Calgary, Canada %P 1 - 7 %8 07/2009 %@ 978-1-4244-4241-6 %R 10.1109/PES.2009.5275924