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.

10aAA09-00210aAARD10aAutomatic Switchable Network (ASN)10aoscillations1 aZhang, Peng1 aZhou, Ning1 aAbdollahi, Ali uhttps://certs.lbl.gov/publications/generalized-subspace-least-mean02020nas a2200253 4500008003900000022001400039245008400053210006900137260001200206300001400218490000700232520124900239653001301488653000901501653003901510653003601549653001801585100001701603700001501620700002101635700001801656700002001674856007201694 2013 d a0885-895000aMode shape estimation algorithms under ambient conditions: A comparative review0 aMode shape estimation algorithms under ambient conditions A comp c05/2013 a779 - 7870 v283 aThis 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.10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10aphasor measurement units (PMUs)10apower systems1 aDosiek, Luke1 aZhou, Ning1 aPierre, John, W.1 aHuang, Zhenyu1 aTrudnowski, Dan uhttps://certs.lbl.gov/publications/mode-shape-estimation-algorithms01837nas a2200241 4500008003900000022001400039245008100053210006900134260001200203300001600215490000700231520109000238653001301328653000901341653003901350653003601389653002701425653001001452100001501462700002101477700002001498856007701518 2012 d a0885-895000aA Stepwise Regression Method for Estimating Dominant Electromechanical Modes0 aStepwise Regression Method for Estimating Dominant Electromechan c05/2012 a1051 - 10590 v273 aProny 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.10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10aphasor measurement units (PMUs)10aPower system stability10aRTGRM1 aZhou, Ning1 aPierre, John, W.1 aTrudnowski, Dan uhttps://certs.lbl.gov/publications/stepwise-regression-method-estimating01513nas a2200217 4500008003900000020002200039245007900061210006900140260003500209300001000244520080700254653001301061653000901074653003901083653001801122653002801140100001601168700001501184700002101199856007501220 2011 d a978-1-4577-0417-800aEvaluation of mode estimation accuracy for small-signal stability analysis0 aEvaluation of mode estimation accuracy for smallsignal stability aBoston, MA, USAbIEEEc08/2011 a1 - 73 aThis 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.10aAA09-00210aAARD10aAutomatic Switchable Network (ASN)10aload modeling10apower system monitoring1 aFollum, Jim1 aZhou, Ning1 aPierre, John, W. uhttps://certs.lbl.gov/publications/evaluation-mode-estimation-accuracy02070nas a2200277 4500008003900000020002200039245008600061210006900147260003600216300001000252520120300262653001301465653000901478653003901487653001201526653002601538653002701564653000901591100001601600700002201616700001901638700001501657700001801672700002501690856007701715 2011 d a978-1-4577-1000-100aThe influence of topology changes on inter-area oscillation modes and mode shapes0 ainfluence of topology changes on interarea oscillation modes and aDetroit, MI, USAbIEEEc07/2011 a1 - 73 aThe 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.

10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10adamping10apower grid operations10aPower system stability10aWECC1 aChen, Yousu1 aFuller, Jason, C.1 aDiao, Ruisheng1 aZhou, Ning1 aHuang, Zhenyu1 aTuffner, Francis, K. uhttps://certs.lbl.gov/publications/influence-topology-changes-inter-area01571nas a2200241 4500008003900000020002200039245008200061210006900143260003600212300001000248520076300258653001301021653000901034653003901043653003601082653002901118100001501147700001801162700002501180700002001205700002901225856007501254 2011 d a978-1-4577-1000-100aA modified stepwise linear regression method for estimating modal sensitivity0 amodified stepwise linear regression method for estimating modal aDetroit, MI, USAbIEEEc07/2011 a1 - 73 aSmall 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.

10aAA09-00210aAARD10aAutomatic Switchable Network (ASN)10aphasor measurement units (PMUs)10apower system reliability1 aZhou, Ning1 aHuang, Zhenyu1 aTuffner, Francis, K.1 aTrudnowski, Dan1 aMittelstadt, William, A. uhttps://certs.lbl.gov/publications/modified-stepwise-linear-regression01950nas a2200265 4500008003900000020002200039245009000061210006900151260002900220300001000249520110800259653001301367653000901380653003901389653001201428653001701440653002501457653002601482653002701508100001801535700001501553700002501568700002001593856007101613 2011 d a978-1-4244-9618-100aUse of Modal Sensitivity to Operating Conditions for Damping Control in Power Systems0 aUse of Modal Sensitivity to Operating Conditions for Damping Con aKauai, HIbIEEEc01/2011 a1 - 93 aSmall 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.

10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10adamping10aoscillations10apower system control10aPower system dynamics10aPower system stability1 aHuang, Zhenyu1 aZhou, Ning1 aTuffner, Francis, K.1 aTrudnowski, Dan uhttps://certs.lbl.gov/publications/use-modal-sensitivity-operating01760nas a2200253 4500008003900000020002200039245011400061210006900175260003500244300001000279520090000289653001301189653000901202653003901211653002101250653003601271653002801307100001501335700001801350700002501368700002101393700002201414856007001436 2010 d a978-1-4244-6549-100aAutomatic implementation of Prony analysis for electromechanical mode identification from phasor measurements0 aAutomatic implementation of Prony analysis for electromechanical aMinneapolis, MNbIEEEc07/2010 a1 - 83 aSmall 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.

10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10agrid reliability10aphasor measurement units (PMUs)10apower system monitoring1 aZhou, Ning1 aHuang, Zhenyu1 aTuffner, Francis, K.1 aPierre, John, W.1 aJin, Shuangshuang uhttps://certs.lbl.gov/publications/automatic-implementation-prony02029nas a2200277 4500008003900000020002200039245007200061210006900133260003500202300001000237520114200247653001301389653000901402653003901411653003601450653002701486100001801513700001501531700002501546700001601571700002001587700002901607700002001636700002301656856007201679 2010 d a978-1-4244-6549-100aImproving small signal stability through operating point adjustment0 aImproving small signal stability through operating point adjustm aMinneapolis, MNbIEEEc07/2010 a1 - 83 aModeMeter 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.10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10aphasor measurement units (PMUs)10aPower system stability1 aHuang, Zhenyu1 aZhou, Ning1 aTuffner, Francis, K.1 aChen, Yousu1 aTrudnowski, Dan1 aMittelstadt, William, A.1 aHauer, John, F.1 aDagle, Jeffery, E. uhttps://certs.lbl.gov/publications/improving-small-signal-stability01314nas a2200229 4500008003900000020002200039245011100061210006900172260004000241300001000281520052500291653001300816653000900829653003900838653002600877100002500903700001800928700001500946700002500961700002400986856007401010 2010 d a978-1-4244-6546-000aInitial studies on actionable control for improving small signal stability in interconnected power systems0 aInitial studies on actionable control for improving small signal aNew Orleans, LA, USAbIEEEc04/2010 a1 - 63 aPower 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.

10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10aPower system modeling1 aTuffner, Francis, K.1 aHuang, Zhenyu1 aZhou, Ning1 aGuttromson, Ross, T.1 aJayantilal, Avnaesh uhttps://certs.lbl.gov/publications/initial-studies-actionable-control02086nas a2200253 4500008003900000022001400039245005800053210005800111260001200169300001400181490000700195520135600202653001301558653000901571653003901580653000901619100002101628700001501649700002501664700002001689700002001709700002901729856007401758 2010 d a0885-895000aProbing Signal Design for Power System Identification0 aProbing Signal Design for Power System Identification c05/2010 a835 - 8430 v253 aThis 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.10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10aWECC1 aPierre, John, W.1 aZhou, Ning1 aTuffner, Francis, K.1 aHauer, John, F.1 aTrudnowski, Dan1 aMittelstadt, William, A. uhttps://certs.lbl.gov/publications/probing-signal-design-power-system01776nas a2200241 4500008003900000020002200039245010900061210006900170260003500239300001000274520096800284653001301252653000901265653003901274653003601313653002601349100001501375700001801390700001701408700002001425700002101445856006801466 2009 d a978-1-4244-4241-600aElectromechanical mode shape estimation based on transfer function identification using PMU measurements0 aElectromechanical mode shape estimation based on transfer functi aCalgary, CanadabIEEEc07/2009 a1 - 73 aPower 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.10aAA07-00110aAARD10aAutomatic Switchable Network (ASN)10aphasor measurement units (PMUs)10aPower system modeling1 aZhou, Ning1 aHuang, Zhenyu1 aDosiek, Luke1 aTrudnowski, Dan1 aPierre, John, W. uhttps://certs.lbl.gov/publications/electromechanical-mode-shape