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Synchrophasor-Based Monitoring of Critical Generator Buses for Transient Stability Yunhui Wu, Student Member, IEEE, Mohamad Musavi, Senior Member, IEEE, and Paul Lerley, Senior Member, IEEE
Abstract—Many interconnected power systems are constructed to meet the ever-increasing electric power transfer demand. A disturbance anywhere in such an interconnected system will directly influence the power transfer capability of major transfer interfaces, as well as the transient stability of the system. Instead of the current practice of monitoring the power transfer limit on a given interface, this paper proposes a real-time synchrophasor method to monitor the stability margin using generator phase angle differences and alert operators of the potential risk to the system at the steady state operation. This is accomplished by developing an algorithm to directly correlate the phase angle separation of critical generator bus pairs to power transfer on major interfaces. These critical generator bus pairs are selected systematically through transient stability simulation. The Eastern North American power system is used as a platform to illustrate the utility of the proposed method. Index Terms—Identification of critical buses, phasor measurement unit (PMU), power system monitoring, transient stability margin.
I. INTRODUCTION
P
OWER transfer between interconnected areas and its impact on system stability plays an important role in present power grid as the demand for electric consumption increases. When analyzing the performance of a power system it is common to subdivide the network into significant geographic areas and monitor the power flows across the transmission lines interconnecting these geographic areas. The power transfer limits in each of the interfaces are determined by the regional independent system operators (ISOs), based on offline steady state and transient stability analysis. Two power transfer limits are considered in any power system: the steady-state limit (thermal and voltage) and the transient stability limit. These power limits are monitored by the energy management system (EMS) and evaluated by the system operators to insure the system reliability and stability. The focus of this research is on the transient stability limit. Most of the research on monitoring and prediction of transient stability considers three major methods: 1) observing the Manuscript received June 10, 2014; revised October 10, 2014 and December 16, 2014; accepted January 08, 2015. Date of publication February 06, 2015; date of current version December 18, 2015. This work was supported by Maine Utilities-University Synchrophasor Consortium and Central Maine Power. Paper no. TPWRS-00785-2014. Y. Wu and M. Musavi are with the Electrical Engineering Department, University of Maine, Orono, ME 04469 USA (e-mail:
[email protected]). P. Lerley is with RLC Engineering, Augusta, ME 04347 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2015.2395955
phase angle separation from the phase angle reference of the system [1]; 2) using the energy function as an index to estimate system transient stability [2]; and 3) quantifying the transient stability profile by observing system trajectories [3]. A critical measure in system stability is the separation of phase angles in generator buses, which is directly related to the power transfer. The North American Northeast blackout in 2003 [4] illustrated the growing separation of phase angle difference between two buses in different areas before the collapse of the system. The phasor measurement unit (PMU) is considered to be one of the most effective measuring devices in power system monitoring and control [5] in a wide area network (WAN). As compared to the supervisory control and data acquisition (SCADA) data, the significance of PMU is its notable capability to provide frequency, voltage and current information at a high sampling rate using a global positioning system (GPS) reference source for synchronization. Most commercially available PMUs today can measure data at a rate of at least 30 samples per second. Depending on users' requirement and new applications, some PMUs will be operated at a rate of 60 samples per second [6]. The high speed sampling rate of PMUs will allow operators to monitor the steady state and dynamic oscillation of power systems in real-time. Researchers have investigated many monitoring methods to estimate system stability from synchrophasor data. PMU-based monitoring index can be basically categorized based on phase angle differences, voltage magnitudes, frequency or rate of change of frequency [7], [8]. Recent advances in the use of PMU data to monitor system stability are described in [9]–[16]. Hamon et al. [9] derived a second-order approximations to find the stability boundaries in the parameter space and used the approximations to solve a stochastic optimal power flow problem. Dobson [10] introduced a concept of voltage phase angle across a cutest of lines for system monitoring based on PMU measurements and circuit theory. Sun et al. [11] introduced a statistical framework of fast-slow systems and critical slowing down to assess the stability behavior of a system under stress. A method to monitor rotor angle dynamics using Lyapunov exponent is introduced in [13]. The above researches have investigated stability boundary and monitoring methods for a power system. But very little work has been done to correlate the power flow on an interface to the transient stability of a power system through separation of generator phase angles. For instance, Bhargava [17] pointed that steady state phase angle differences provide better resolution in real-time monitoring of critical buses than power flow measurement. Currently, ISOs place power flow limits on major interfaces to ensure that the
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system would remain stable in the event of an extreme contingency anywhere in the network. These interfaces are intuitively selected by system operators and the corresponding limits are based on offline simulations for pre-defined contingencies. Operators in the control room use these power flow limits to make sure that the system is in stable operation. Although, the current methodology provides system stability, it doesn't directly link the cause of instability to any particular generator. At present, people rely on expertise's experience with the system to select critical buses for system monitoring. Very little work has been done to develop a scientific methodology in finding critical buses based on the dynamic performance of generators in the event of contingencies. In this paper, we propose a stability margin monitoring method by directly linking power transfer in an interface with the phase angle difference between critical generator bus pairs in the network. The novelty of the proposed approach is to use the phase angle difference of critical generator bus pairs instead of the power flow to monitor the transient stability margin of a power system. Generator phase angles, which are the cause of instability, can be measured directly by PMUs to alarm the operators at steady state operation. The use of an alarm during the steady state operation indicates potential risk for violating the system transient stability. In most cases the system operators take action to re-dispatch generations when the alarm limit is reached in matter of minutes to ensure system stability in the event of a contingency. Furthermore, instead of using the widely used intuitive selection of significant interfaces, we determine the critical bus pairs through systematic analysis of transient stability simulations. This analysis can be performed effectively through a batch process. Therefore, another novelty proposed in this paper is the application of a scientific method to select critical generator bus pairs for transient stability consideration. The basic concept in transient stability margin and its monitoring with synchrophasor data are described in Sections II–IV. Application of the methodology on the Eastern North American Power System (ENAPS) and the results are presented in Section V. Section VI will give the conclusion.
Fig. 1. Flow chart of online transient stability monitoring.
selection process, a geographical generation dispatch method, as described in Section V, has been used. Once the critical bus pairs have been identified, the steady state performance of phase angle differences for these buses will be monitored online by using PMUs. The transient stability margin can be directly observed from monitoring the critical bus pairs at steady state. By checking the margin, a stable or unstable decision can be made for the current operational condition. It is assumed that the system will be operated below the alarm limit during steady state and if any contingency were to occur the system will remain stable. The alarm will alert operators that the system will be in potential instability risk if the worst contingency happens. Otherwise, the monitoring continues using the online PMU measurements until the operational condition is updated by the EMS. The above process is given in the flowchart of Fig. 1 and described in details in the following sections.
II. MONITORING SCHEME
III. IDENTIFICATION OF CRITICAL BUS PAIRS
This paper presents an online transient stability monitoring method using PMU data. This is based on the off-line identification of critical generator bus pairs while incrementally changing power transfer on an interface by considering different contingencies. Off-line contingencies can be conducted under different operational conditions including generation dispatch, topology change, load level, etc. The updated information can be obtained from SCADA every 5 min [18]. Contingencies are selected from a pre-defined set of relatively worst case scenarios, including most of the 3-phase faults and cascaded faults, based on the practical expertise of system planners, operators and system's historical performance. For each operational condition, the critical bus pairs are found for all contingencies while the power transfer is ramped up on the interface taking the system from a stable to an unstable condition. To consider the sensitivity of the critical bus pair
As the power transfer in an interface increases, the absolute phase angle differences between system generators will increase until the stability of system could not be maintained. This performance can be observed by the first swing of a set of generations that lose synchronization first. During the transient oscillation, the peak values of phase angle separation in stable case, shaped by the complex interaction of the generators inertia, their control devices, the system topology, and the fault characteristics and severity, are found as one significant parameter that will contribute to defining the system stability limit. The response time of phase angle separation starting from fault clearing time to the time that instability occurs is considered as another important parameter to define critical bus pairs. Critical buses indicating the stability limit of a system are found out of a comparative analysis considering both the maximum peak value and the fastest response time under all pre-defined contingencies. Since
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method to sort the impact of each GBP for all contingencies using the following equation:
(3) where matrix is derived from matrix components based on
but with 0 and 1
if GBP ( ) is present in if GBP ( ) is NOT present in
Fig. 2. Parameters for finding critical bus pairs.
we consider all possible combinations between every two gengenerator bus pairs (GBPs), erators, there will be as indicated in (1):
where and is the sorted order identifying the row of the matrix. Therefore, the calculated indicates the importance of each GBP to all contingencies. The smaller the value of is the higher impact the GBP would have on stability for all contingencies. For instance, a is more critical to the system stability GPB with a than a GBP with a . Since there are combinations of GBPs, we limit our analysis to those generators that satisfy the following conditions:
(1) Equation (2) is used to sort all the GBPs in (1), from the highest to the lowest impact on system stability, under the contingency: (2) ;
;
; ; , where and are the absolute values of the phase angle difference between the th and th generator buses for the boundary interface power transfer (stability limit) at the time when the phase angle difference is at its maximum value ) and at the fault clearing time . ( is the time when the value of the phase angle difference for the unstable interface power transfer is equal to the phase angle . difference for the boundary interface power transfer at Fig. 2 shows phase angle difference of one pair of generators for a stable (lower curve), a boundary (middle curve), and unstable power transfer (upper curve) for one operational condition and one contingency. This figure is used to clarify the components of (2). matrix in (2) has rows Therefore, the (sorted GBPs) and columns (contingencies). Note that the first row of INDEX gives the highest impact GBPs for all predefined contingencies; the second row gives the second highest ) impact GBPs, and so on. We use a Weighted Mean (
, refer to the thresholds of phase angle difference and response time respectively. Their values could be modified to adapt the method to different power systems. We will employ and in our study limiting our GBPs to 5. In term of physical description, these GBPs can be expressed as having the shortest margin from the boundary of stability. IV. PROPOSED MONITORING METHOD Considering the power transfer in an interface, there is a relationship between this power transfer and the phase angle difference of generator bus pairs in the system while a contingency occurs. This can be described by (4): (4) is the phase where is the power transfer in the interface, angle difference of two generator pairs, is the total combination of generator pairs, and is the relationship, which depends on the system operational condition and the assumed contingency used in the dynamic analysis. A. Pre-Fault Correlation of Phase Angle Difference to Power Transfer In this section, we will discuss the relationship between the steady state phase angle difference of generator pairs and the real power changes in an interface, as presented in (4). As an example, a section of a power system, shown in Fig. 3, with two generators and and an interface consisting of only
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Note that coefficient in the above equation is constant and depends on system topology, dispatch, and availability of a load-flow solution. In general, the above relationship can be described by (14):
Fig. 3. Section of a power system.
(14) one line between buses 2 and 3, is used to correlate the interface power transfer and phase angle difference between the two generator buses ( ). Empirically, phase angles across a transmission line are usually kept below 44 in order to insure the steady-state rotor angle stability [19]. In a power system at steady state, like the one used in this study, the phase angle difference across every transmission line changes about 2 when power transfer on the interface changes by 100 MW. For , the power transfer (4) can be approximated linearly [20] by
where is the phase angle of one critical bus (start bus) and is phase angle of the other critical bus (end bus). In reality, an interface may have several transmission lines. The total power transfer on the interface, , is then the linear sum of power transfers on all transmission lines and still a linear relationship to the phase angle difference of the generator pair:
(5) (15) therefore, the power transfers between every two directly connected buses are (6) (7)
where is a function of and . This linear characteristic between phase angle difference and power transfer on an interface under the assumed circumstances has also been observed experimentally, as demonstrated in Section V.
(8)
B. Post-Fault Correlation of Phase Angle Difference to Power Transfer
(9)
Consider a contingency occurs somewhere in the power system impacting the dynamics of critical generators, such as the two machines in Fig. 3. For this two synchronous machine system, ignoring the damping factor, we have a pair of power swing (16) and (17):
Summing (6)–(8), we will get
We can assume that the coefficients of power transfer in (9) are constant:
(16) (17) Once the topology and generation dispatch are fixed, power transfer on the interface usually changes incrementally in the same transfer direction. Under these circumstances, we assume that the power distribution factor is approximately constant. The correlation between each power transfer is formulated by (10)–(12): (10)
where and are the rotor angles of the two synchronous machines. It is notationally convenient to define , where and are the per unit inertia constant and synchronous frequency, respectively. is the electrical power and is the mechanical power supplied by the turbine. The two (16) and (17) can be replaced by a single equation in the intermodal angle , as in (18):
(11)
(18)
(12) . Substituting where is ratio of power distribution; , , and , , into (9), we will get a linear relationship between the real power ( ) on the interface and phase angle difference of ( ):
(13)
Equation (18) can be presented as (19) The critical factor determining the stability of (19) under a system disturbance is the potential energy [21]. Assume the generator bus phase angle difference ( ) approximately equals to rotor angle difference ( ). The potential energy of (19) under
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Fig. 5. Phase angle difference relationship with the interface power transfer of bus 1 and 4. Fig. 4. Interface power transfer relationship with phase angle difference.
a particular power transfer on the interface is presented by (20) and shown as the sinusoidal curve in Fig. 4: (20) equals to , where In (20) the pre-fault steady state has a local minimum corresponding to . The and happen at the points where total energy equals to , where the kinetic energy is zero. The total energy can be calculated by the summation of kinetic energy and potential energy:
(21) As proved in Section IV-A, during the pre-fault steady state, power transfer levels in the interface have a linear correlation with phase angle differences of generation buses. Therefore, setting , the potential energy will be
(22) As power transfer level in the interface increases from to , the steady state phase shift will change from to resulting in a potential energy shift, as shown by in Fig. 4. As power transfer continuously increases, the phase angle difference increases to a point beyond which the system becomes unstable. The potential energy functions for this threshold value and immediately after this point are indicated by and . As the result, the total energy will correspondingly increase. This has been demonstrated as , , , in Fig. 4. Note that these total energy levels are constant, as indicated by the horizontal lines in Fig. 4,
due to the lossless assumption for the power system. Using (21), we can calculate the maximum and minimum phase angle differences under different power transfer levels. These minimum and maximum values are shown in Fig. 4 as the intersections of the horizontal total energy levels with the sinusoidal potential energy functions. Projecting these values onto the plane will result in a stability region between the lower and upper boundaries, as shown in the lower part of Fig. 4. A simple change of axes of the lower part of Fig. 4 results in Fig. 5, which has been used in the rest of this paper for monitoring transient stability margin. Note that this boundary is only for a particular contingency under different power transfer levels. For a system with damping and power loss, is no longer a constant under each power transfer level. Instead, we will have a slowly dropping energy that will consequently decrease the swing in phase angle amplitude. In this case, the maximum and minimum values become closer to each other, effectively narrowing the band observed in Fig. 5. The derivative of the total energy for this case will be negative [21]. C. Definition of Stability Region Considering all the combination of absolute phase angle differences on every two generation buses, the upper and lower boundaries for a random contingency are indicated as the dotdash curves in Fig. 6. The lower boundary among all these combinations could almost be zero, on the horizontal axis, because some generators may have the same swing, such as two or more generators with the same inertia connected to the same bus. The upper boundary identifies the performance of the phase angle difference of two generators that exhibit the largest swing angle in the event of the contingency. This boundary curve can be used to define the transient stability limit of the system for different power transfers on the interface. The upper and lower boundary may change its shape under different system topology and generation dispatches. For all possible contingencies under the same topology and dispatches, we will have different nonlinear relationships similar to (4) resulting in different upper and lower boundaries. An example of
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D. Monitoring Stability Margin Based on Critical Bus Pairs
Fig. 6. Phase angle difference relationship with the interface power transfer for all generator bus pairs.
Fig. 7. Approximated stability/instability region.
the worst contingency with the highest upper boundary is shown as the solid curve in Fig. 6. This provides the maximum phase angle oscillations and will be used to define the stability limit of a system. The upper and lower boundaries of one contingency can be considered as the intersection of a plane with the 3-D surface, Fig. 7, (23): (23) where and are the power transfer and phase angle difference; is the dimension indicating a correlation of and under various contingences and represents the No. of these contingences. A severe contingency (e.g., longer fault clearing time or cascade faults) will elongate and reduce the region of the 3-D surface. Changing the system dispatch or topology may result in changing the size and shape of the 3-D surface.
This part describes how to use the transient stability limit defined by the worst contingency in Section IV-C to monitor transient stability margin of a system using the critical bus pairs. Consider an incremental power transfers on the interface, as presented by , in Fig. 6. The relationship between these power transfers and the pre-fault phase angle differences of the critical pair is also shown in Fig. 6 by a linear dashed line between the lower and upper boundaries going through . The corresponding phase angle differences are shown on the vertical axis. The stability margin of the system at any operating point is defined as the distance between the phase angle differences of the critical generator pair at the operating point to the stability limit for the worst contingencies. This is also demonstrated in Fig. 6. The stability limit, , is the intersection of a horizontal line, dashed line in Fig. 6, with the upper boundary for the worst contingency at the maximum limit of power transfer, . For a pre-fault operating condition corresponding to a power transfer and a phase angle difference , the stability margin is ( ). As the power transfer increases to , the operational condition varies from to accordingly, and the stability margin for monitoring will become . Finally the power transfer gets to the stability limit . If more power is pushed onto the interface, phase angle difference of the critical buses will increase beyond the stability limit and the relevant generations behind these buses will no longer maintain synchronism and lead to system collapse in the event of the worst contingency. Therefore, corresponding to power transfer limit is defined as the alarm point. The real time operational conditions of the critical buses can be obtained from PMUs and monitored by the operators. Using these pre-fault values, operators would be able to monitor how far away the present power system is from the stability limit. As a contingency occurs, the stability margin corresponding to the dynamic performance of the critical bus pair will also be observed using the proposed monitoring method. Therefore, instead of the currently used power transfer limits, the phase angle difference of critical bus pair can be used for monitoring system transient stability. V. CASE STUDIES AND SIMULATION RESULTS The proposed approach is demonstrated using ENAPS as shown in Fig. 8. The entire Maine power system, the upper section of ENAPS, with 152 generators and hundreds of transmission lines, is used as the area of interest and faults were simulated at the other parts of ENAPS. Power system of Maine can be considered as a relative light load area that basically plays a role of power transfer path from Canada to Southern New England. There are three major transmission interfaces in Maine as shown by dotted lines: Interface I, Interface II, and Interface III. We will focus on Interface I in this paper. The system topology and load levels inside of the Maine power grid are assumed fixed throughout the experiments. A. Geographical Generation Dispatch Power system of Maine was geographically divided into 4 regions A, B, C, and D shown in Fig. 9.
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TABLE I GENERATION DISPATCH SUMMARY
TABLE II REAL POWER TRANSFER CAPABILITY ON INTERFACE UNDER EACH CONTINGENCY
Fig. 8. Eastern North American Power System.
farms in the Maine power system. These wind farms are observed having a faster response and bigger oscillation than other conventional generations. In order to investigate the impact of renewable energy on identification of critical buses, we turned all wind farms on in region A, B, C, D which is referred to dispatch D6. Please note that power transfer changes on the interface are due to supply changes from Canada and not dispatch changes in Maine. B. Contingency Analysis
Fig. 9. Geographical dispatch regions in Maine.
For contingency analysis, eight 3-phase faults at different locations and clearing times, marked as #1 to #8, are studied from a pre-defined contingency list [22]. Power transfer on interface was gradually increased from 0 MW to 1500 MW, with interval value of 100 MW. Stability limit of each contingency is simulated by conducting Siemens PSS/E v30 dynamic module. Table II describes the contingencies giving the fault clearing time and the interface maximum power transfer capacity under the given contingency. The severity of each contingency could be found by ranking the value of power transfer limit. The contingency with the lowest value of power transfer limit is considered to be the worst case, contingency #8 in Table II. Note that each transfer limit, which was resulted from the simulation of the system, provides the maximum transfer beyond which the system would become unstable if the contingency occurs. C. Critical Bus Pairs
The generation is dispatched based on different combinations of generators in these four regions resulting in six dispatches D1-D6. Descriptions of these six dispatches are listed in Table I. For instance, the description of dispatch D1 can be interpreted as to increase all the generations in region B to their maximum capacity and decrease the same amount of power in region A. Renewable energy in a power system is usually considered as a generation with small inertia and power capacity, such as wind
fault values of the phase angle differences are increased as the power transfer increases. The critical bus pairs for all contingencies for one dispatch (D1) are found using the model explained above in Section III. The first 10 bus pairs with relatively higher ranking for each contingency are selected. Five critical bus pairs from among all contingencies are found using a weighted mean statistical approach. These 5 critical bus pairs are identified by ranking as {#30-#68, #4-#23, #56-#108, #14-#115, #76-#98}.
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Fig. 11. Transient stability margin monitoring of the most critical bus pair.
D. System Transient Stability Monitoring Fig. 10. Phase angle difference of critical bus pair #30-#68 w.r.t different power levels in a time frame of 20 s. TABLE III CRITICAL BUSES AND POWER TRANSFER LIMIT W.R.T DIFFERENT GENERATION DISPATCHES
The most critical bus pair is #30-#68, which was for contingency #8. Note that bus #68 is a wind farm in region D, and the other one #30 is a conventional generator in region C. The performance of this pair is shown in Fig. 10 for power transfers ranging from 0–1300 MW. The critical bus pair dynamic performance for power transfer of zero through the interface, marked as “P000” in Fig. 10, is stable in the event of the worst contingency. As the power transfer is increased, the transient performance is changed. The instability happens when interface power transfer increases from 1200 MW to 1300 MW. Another observation is that the preSimilar results were obtained for other generation dispatches (D2-D6). Table III shows the most critical bus pair from dispatch D1-D6. Except for dispatch D5, the critical buses for other dispatches are the same. This result indicates that critical bus pairs may vary for different dispatches. It is therefore necessary to run the critical bus pair identifier when generation dispatches change. Another note, which was expected, is that bus #68 that appears in all dispatches, except for D5, is a wind farm.
The transient stability margins from simulation results for the system under study are shown in Fig. 11. The dotted horizontal “Alarm” line shows that the stability limit of power transfer on the interface is 1200 MW corresponding to nearly 140 phase angle difference of the critical bus pair. The pre-fault values of each operating condition are shown on the black solid line as , , , to . Please note that the relatively high phase angle difference between the two critical generator bus pair, such as is 119 , is due to the phase shift by three phase-shifting transformers between these generators. The stability margin between phase angle difference and the threshold value indicates how far the system is away from the stability limit at any given operation point. Obviously, as more power is transferred on the interface, the stability margin will decrease until the system gets to the alarm point . When a contingency occurs, due to the change of the system configurations, phase angle difference will response to this change and begin to oscillate. Its dynamic transient stability margin could be also observed in Fig. 11. As mentioned in Section IV, using phase angle measurements from the PMUs, this chart will help the operators to monitor system performance in real-time while providing the stability margin for the current operational condition. VI. CONCLUSIONS This paper presents a method for online monitoring of system transient stability limits. Instead of using power flow through the intuitively selected interface lines, we use the phase angle differences between critical generator bus pairs to monitor the transient stability margin of a power system. A scientific method is proposed to select critical generator bus pairs based on the maximum swing of phase angle differences and the fastest response time to the system instability. Boundaries of stability for a power system are defined for the worst contingency under current operational conditions. The relationship between power transfer in an interface and phase angle difference of critical generator bus pairs is developed and used for setting transient stability limit. The advantage of this approach is in providing direct link to the generator pairs that cause the risk of instability, hence, enabling
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the operators to make appropriate generation dispatches. Using the proposed method, PMUs can be installed at the critical generators to monitor system transient stability. A case study has been presented to demonstrate the effectiveness the proposed methodology. ACKNOWLEDGMENT The authors would like to thank B. Conroy, B. Huntley, C. Beveridge, and T. Vogel of Central Maine Power Company and W. Whittier of RLC Engineering for their financial support and technical expertise. REFERENCES [1] M. Sherwood, D. Hu, and V. Venkatasubramanian, “Real-time detection of angle instability using synchrophasors and action principle,” in Proc. 2007 iREP Symp.—Bulk Power System Dynamics and Control—VII, Charleston, SC, USA, Aug. 2007. [2] J. H. Chow, A. Chakrabortty, M. Arcak, B. Bhargava, and A. Salazar, “Synchronized phasor data based energy function analysis of dominant power transfer paths in large power systems,” IEEE Trans. Power Syst., vol. 22, no. 2, pp. 727–734, May 2007. [3] A. D. Rajapakse, F. Gomez, K. Nanayakkara, P. A. Crossley, and V. V. Terzija, “Rotor angle instability prediction using post-disturbance voltage trajectories,” IEEE Trans. Power Syst., vol. 25, no. 2, pp. 947–956, May 2010. [4] S. Abraham and J. Efford, “Final Report on the August 14, 2003 Blackout in the United States and Canada,” US-Canada Power System Outage Task Force, 2004. [5] A. G. Phadke, “Synchronized phasor measurements in power systems,” IEEE Comput. Applicat. Power, vol. 6, no. 2, pp. 10–15, 1993. [6] “Real-Time Application of Synchrophasors for Improving Reliability,” North American Electric Reliability Corporation (NERC), 2010. [7] Y. V. Makarov, P. Du, S. Lu, T. B. Nguyen, X. Guo, J. W. Burns, J. F. Gronquist, and M. A. Pai, “PMU-based wide-area security assessment: Concept, method, and implementation,” IEEE Trans. Smart Grid, vol. 3, no. 3, pp. 1325–1332, Sep. 2012. [8] J.-H. Liu and C.-C. Chu, “Wide-area measurement-based voltage stability Indicators by modified coupled single-port models,” IEEE Trans. Power Syst., vol. 29, no. 2, pp. 756–764, Mar. 2014. [9] C. Hamon, M. Perninge, and L. Soder, “A stochastic optimal power flow problem with stability constraints—Part I: Approximating the stability boundary,” IEEE Trans. Power Syst., vol. 28, no. 2, pp. 1839–1848, May 2013. [10] I. Dobson, “Voltages across an area of a network,” IEEE Trans. Power Syst., vol. 27, no. 2, pp. 993–1002, May 2012. [11] K. Sun, X. Luo, and J. Wong, “Early warning of wide-area angular stability problems using synchrophasors,” in Proc. IEEE PES General Meeting, San Diego, CA, USA, 2012. [12] H. Deng, J. Zhao, X. Wu, and K. Men, “Real time transient instability detection based on trajectory characteristics and transient energy,” in Proc. IEEE PES General Meeting, 2012. [13] J. Yan, C. Liu, and U. Vaidya, “PMU-based monitoring of rotor angle dynamics,” IEEE Trans. Power Syst., vol. 26, no. 4, pp. 2125–2133, Nov. 2011. [14] N. Kakimoto, M. Sugumi, T. Makino, and K. Tomiyama, “Monitoring of interarea oscillation mode by synchronized phasor measurement,” IEEE Trans. Power Syst., vol. 21, no. 1, pp. 260–268, Feb. 2006.
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[15] I. Kamwa et al., “Wide-area monitoring and control at Hydro-Quebec: Past, present and future,” in Proc. IEEE PES General Meeting, Jun. 2006. [16] K. Sun, S. Likhate, V. Vittal, V. S. Kolluri, and S. Mandal, “An online dynamic security assessment scheme using phasor measurements and decision trees,” IEEE Trans. Power Syst., vol. 22, no. 4, pp. 1935–1943, Nov. 2007. [17] Eastern Interconnection Phase Angle Base Lining Study. Washington, DC, USA, US Department of Energy, 2013. [18] M. Ahlstrom, D. Bartlett, and C. Collier, “Efficiently integrating wind energy and wind forecasts,” IEEE PowerEnergy Mag., vol. Nov./Dec., pp. 45–52, 2013. [19] R. D. Dunlop, R. Gutman, and P. P. Marchenko, “Analytical development of loadability characteristics for EHV and UHV transmission lines,” IEEE Trans. Power App. Syst., vol. PAS-98, no. 2, pp. 606–617, Mar./Apr. 1979. [20] C. W. Taylor, Power System Voltage Stability. New York, NY, USA: McGraw-Hill, 1994. [21] A. R. Bergen and V. Vittal, Power System Analysis. Englewood Cliffs, NJ, USA: Prentice Hall, 2000. [22] RLC-Engineering, “Maine Power Reliability Program (MPRP) North to South Steady State Transfer Limits and Incremental Stability Performance Study”. Augusta, ME, USA: RLC-Engineering, pp. 12, 2012.
Yunhui Wu (S’12) received the B.S. and M.S. degrees in engineering college from Shanghai Ocean University, Shanghai, China, in 2007 and 2010, respectively. Currently she is pursuing the Ph.D. degree at the Department of Electrical and Computer Engineering (with a minor in mechanical engineering), University of Maine, Orono, ME, USA. Her research areas include power system stability assessment, state estimation and application of synchrophasor and artificial neural networks in the smart grid.
Mohamad Musavi (SM’02) received the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, MI, USA, in 1979 and 1983, respectively. He is currently the Associate Dean of the College of Engineering and a Professor of electrical and computer engineering at the University of Maine, Orono, ME, USA. His research interest is in the development of neural networks in a number of areas including power systems, smart grid, paper industry, genomics, and other applications.
Paul Lerley (SM’88) received the BTS degree from the Lycée Technique, Strasbourg, France, in 1968 and the BET degree from the University of New Hampshire, Durham, NH, USA, in 1979. He is currently a Senior Power System Engineer at RLC-Engineering. His professional journey included test engineering, power system protection applications, testing and training and currently power system simulations. He served on the PSRC from 1988 to 1999.
