SYSTEMS AND METHODS FOR IDENTIFYING WEAK LINKS IN AN ELECTRICAL POWER SYSTEM

BACKGROUND

[0001] Stability is one of the key issues in modern electrical power systems. As the grid becomes more complex, voltage stability in the grid network becomes even more critical for utilities to provide reliable service. Electrical power systems are monitored and controlled to provide continuous and reliable service; however, system outages may still occur and are often associated with voltage instabilities. Since power system stability is directly linked to networks, loading conditions, changes in the system, and time, it is imperative to sense or predict instability as early as possible. Any error in computing or measuring voltage stability may result in delay in the detection of the voltage instability. Any delay in sensing and engaging counter-measures may further deteriorate the system conditions and can lead to unwanted and uncontrollable collapses, or costlier counter measures.

[0002] The approaches for determining voltage instability may be broadly divided into three categories; first that may require some wide area network information, such as topology, reactive power limits of generators, line impedances, and so on; second that may use local network information, such as power flows over a particular line or voltages and currents at the end buses; and third that may not require any system information and instead relies only on local measurements, such as voltage, current, and rate of change of these quantities.

[0003] The majority of the existing approaches use model-based solutions rather than measurement-based approaches. One such model-based approach uses power flow or continuation power flow to track Power Voltage (PV) curve for voltage instability assessment. One measurement-based approach used in the industry is Thevenin's approach that uses voltage and current values to evaluate voltage instability. Some existing approaches attempt to identify weak links in the system and can be used further to engage counter measures, before the system reaches the voltage instability point.

[0004] The challenge with these existing approaches is that they are computationally cumbersome and not suitable for real-time assessment of voltage instability. Moreover, the existing measurement-based approach needs various parameters such as network parameters, information about the loading condition, changes in controls, outages, and so on for assessing the voltage instability, in addition to parameters such as voltage and current values. Unavailability of any of these parameters or error in computing them may result in inaccurate detection of voltage instability, which may lead to service disruption and therefore loss for both customers and utilities.

BRIEF DESCRIPTION
[0005] In accordance with one embodiment, a method for identifying one or more weak links in an electrical power system is provided. The method includes computing voltage stability indices (VSIL) corresponding to a plurality of links in the electrical power system as a function of phasor values associated with a plurality of buses. Each of the phasor values includes voltage magnitude (Vm) and phase angle (6m), both corresponding to the respective bus. The method further includes identifying the one or more weak links from the plurality of links in the electrical power system based on the computed VSIL.

DRAWINGS
[0006] These and other features and aspects of embodiments of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:

[0007] Fig. 1 is an electrical power system including a bus connected to other buses via transmission or distribution links.

[0008] Fig. 2 depicts a control center system that communicates with monitoring modules for determining one or more weak links and voltage instability in the electrical power system, in accordance with one embodiment.

[0009] Fig. 3 depicts a two-bus electrical system and its equivalent phasor diagram.

[0010] Fig. 4 is a flowchart depicting a method for identification of weak links from a plurality of links and determination of voltage instability in the electrical power system, in accordance with one embodiment.

DETAILED DESCRIPTION
[0011] Unless defined otherwise, technical and scientific terms used herein have the same meaning as is commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terms "first", ''second", and the like, as used herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. Also, the terms "a" and "an" do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced items. The term "or" is meant to be inclusive and mean one, some, or all of the listed items. The use of terms such as "including," "comprising," or "having" and variations thereof herein are meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The terms "module," "processor," "storage unit," "network interface," and "input/output (I/O) interface" may include either a single component or a plurality of components, which are either active, or passive, or both, and are connected or otherwise coupled together to provide the described function. Additionally, for purposes of explanation, specific numbers, components, and configurations are set forth in order to provide a thorough understanding of various embodiments of the invention.

[0012] Various embodiments of the present invention are directed to system and method for determining one or more weak links (hereinafter referred to as weak links) including a single weakest link or multiple weak links in an electrical power system. The term "link" as used herein refers to any electrical line with a pair of buses connected at two ends of that electrical line. The link may also be an electrical component such as a capacitor, a reactor, a switched capacitor (for example, a thyristor switched capacitor), a transformer, with electrical terminals connected to the pair of buses. In one embodiment, the link may be only the electrical line, that is, without any active or reactive power support (for example, capacitors, generators, or so on) between the pair of buses connected at two ends of the electrical line. The reactive power support may be injected into the link to feed power into or to draw power from the link. In embodiments where there are one or more active or reactive power supports between the pair of buses, the electrical line connecting the pair of buses may be divided into multiple links. In one exemplary embodiment, when one or more real or reactive power supports are injected at a same bus 'B31 between a pair of buses 'Bl' and ^BS,1 the electrical line including the buses 'Bl,' "B2! and B3 may be divided into two links; one between the buses 'BT and 'B3\ and the other between the buses 'B3' and 'B2.' In yet another embodiment multiple electrical paths between a pair of buses with at least one path without any real or reactive power support between the pair of buses may define a link. Embodiments of the system and method disclosed herein may ensure that determining the weak links may be further used to implement appropriate counter-measures to reduce or eliminate any unwanted and uncontrollable collapses caused due to delay in the detection of voltage instability.

[0013] Fig. I is an electrical power system 100 (hereinafter referred to as "system 100") including a bus 102 connected to one or more buses 104, 106, 108 and 110 via transmission or distribution links (hereinafter referred to as '"links") 112, 114, 116 and 118, respectively. The system 100 may be a synchronized alternating current (AC) system, in accordance with some embodiments. The system 100 may further include an electrical load 120 connected to the bus 102. The system 100 may further include an electrical power source(s) such as one or more generators 124 that may generate electrical power for the rest of the system 100. Although Fig. 1 illustrates three generators; however, any number of generators may be deployed in the system 100 without deviating from the scope of the invention. Similarly, any number of electrical loads, buses or links may be implemented in the system 100, in accordance with some embodiments of the invention.

[0014] In some embodiments, the system 100 may further include one or more monitoring modules 126 (hereinafter referred to as "monitoring modules 126") that may be configured to determine phasor values associated with a plurality of buses ('m' buses, where m is the number of buses). As shown in Fig. 1, in some embodiments, the plurality of buses (or 'm' buses) may include some or all of the bus 102 and the buses 104, 106, 108 and 110. In one exemplary embodiment, the monitoring modules 126 may be phasor measurement units (PMUs) or relays embedding functionalities of PMUs. In another exemplary embodiment, some or all the phasor values may be obtained from, but not limited to, an energy management system (EMS), a manual input from a utility operator, historical data of the phasor values, or a tool for computing the phasor values, or any combination thereof. In some embodiments, the phasor values may be determined or obtained in real-time. In one embodiment, real-time may refer to occurrence of event instantaneously, for example, in the order of milliseconds or microseconds. In another embodiment, real-time may be near real-time having a predetermined tolerance with respect to instantaneous real-time. In one exemplary embodiment where data is received near real-time, a utility operator or a protection engineer viewing the data may not perceive any delay during display of data.

[0015] In one exemplary embodiment, the phasor value may include voltage magnitude (V,„) determined at an 'mth* bus, and phase angle (8m) determined at the same 'mth' bus. The term "voltage magnitude (Vm)" at the 'mth' bus herein refers to voltage value at the 'mth' bus expressed in per unit (pu) or volt. Until otherwise mentioned, various electrical parameters described herein for computation of voltage stability indices (VSIL) at a plurality of links (such as links 112, 114, 116 and 118) are expressed in pu. The phase angle is expressed herein in degrees or radians. In one embodiment, when the phase angle is measured by the monitoring modules 126, the phasor angle may be measured with respect to a global time reference such as global positioning system (GPS) clock. For example, voltage magnitude and phase angle determined at a bus ;B 1' (one of the "nr buses) are hereinafter interchangeably referred to as V, and 5,, respectively. In some embodiments, the monitoring modules 126 may be configured to measure ail phasor values at the plurality of buses at a same time instance, which may be absolute time or relative time, since these values may differ when measured at different time instances due to, for example, changes in system topology such as addition or removal of reactive power support in the system 100. In another embodiment, some or all the phasor values may be estimated from a state estimator in a control center system such as EMS.

[0016] Fig. 2 depicts a control center system 200 (hereinafter referred to as system 200) that communicates with the monitoring modules 126 for determining weak links and voltage instability in an electrical power system (such as system 100), in accordance with one embodiment. In one exemplary embodiment, the system 200 may be a phasor data concentrator (PDC) or supervisory control and data acquisition/energy management system (SCADA/EMS) that may be configured to control and monitor the monitoring modules 126 and may access the phasor values determined by the monitoring modules 126. In one such embodiment, when the system 200 is a PDC, the system 200 may be further connected to a wide area monitoring system such as SCADA/EMS (not shown in Fig. 2).

[0017] As illustrated in Fig. 2. the system 200 may include a storage unit 204, a processor 206, an I/O interface 208, and a network interface 210. The I/O interface 208 may include one or more human I/O devices, which enable a utility operator or a protection engineer to communicate with the monitoring modules 126 or other communication devices via a communication network 212, in accordance with one embodiment. In an alternate embodiment, the utility operator or the protection engineer may communicate with the monitoring modules 126 or other communication devices from a local or remote workstation 214 via the communication network 212. The communication network 212 may be, for example, a known wired or wireless network using which the system 200 may control and monitor the monitoring modules 126.

[0018] In certain embodiments, the processor 206 may store the received, processed, and transmitted data to, or may read from, the storage unit 204, such as a hard disk drive, a floppy disk drive, a compact disk-read/write (CD-R/W) drive, a digital versatile disc (DVD) drive, a flash drive, or a solid-state storage device. The processor 206 may include, for example, one or more application-specific processors, graphical processing units, digital signal processors, microcomputers, microcontrollers, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or other suitable devices in communication with one or more components of the system 200.

[0019] The processor 206 may include a computation module 216 for analyzing data that is received at and transmitted from the I/O interface 208 or the network interface 210 in the system 200. In some embodiments, the computation module 216 may be configured to compute VS1L (that is, at the plurality of links) as a function of phasor values associated with km' buses. Similar to Fig. 1, as shown in Fig. 2, in some embodiments, the 'm' buses may include some or all of the bus 102 and the buses 104, 106, 108 and 110.

[0020] The determination of phasor values and computation of VSIL are described herein in conjunction with Fig. 3. Fig. 3 depicts a two-bus electrical system 300 and its equivalent phasor diagram 302. As shown in Fig. 3, in some embodiments, the two-bus electrical system 300 may include a power source such as a first generator *G1.' two buses 304 and 306, a link 'L* electrically coupled to the two buses 304 and 306 (interchangeably referred to as "pair of buses'), and a reactive power support such as a second generator 'G2' electrically coupled to the bus 306. Voltage magnitude and phase angle at the bus 304 are represented by '\V and '8,,' respectively; whereas voltage magnitude and phase angle at the bus 306 are represented by 'V2' and 'Si,' respectively. The phasor diagram 302 depicts a phasor angle (5) as an angular separation between the voltage magnitudes *Vi' and ;V2,' where 5= 82 - S,. In some embodiments, the computation module 216 may be configured to compute VSI at the Sink ;L' ('VSliV) connecting the two buses 304 and 306 as a function of voltage magnitudes 'V,' and 'V2' at the buses 304 and 306, respectively, and phase angles 'Sj' and '82' at the buses 304 and 306. respectively. As given in equations 13 and 14, these voltage magnitudes and phase angles may be used to compute VSI at the link "L,* in accordance with some exemplary embodiments. Similarly, in such embodiments, voltage magnitudes and phase angles at respective buses may be used to compute VSIs at other links (in the system 100) connecting such respective buses.

[0021] In another embodiment, VSIs at the plurality of links (VS1L) may be computed as a function of reactive power losses (Qi0Ss) in the plurality of links and power flows (PL) across the same plurality of links. In one exemplary embodiment, as given below in equation 1, a ratio of the reactive power loss (Qioss]) in the link *L' and power flow (PL1) across the link ;L' may be used to determine VSI at the link *L' ('VSIi/), which may be, for example, any ofthe links 112, 114, 116 and 118 in the system 100:
where,
PLI is an equivalent power flow through the link 'L'

[0022] The ratio OIOSSI/PLI in equation I for the two-bus electrical system 300 may be calculated as follows:
where,
Qt2 is reactive power flow from bus 304 to bus 306, and
O21 is reactive power flow from bus 306 to bus 304

[0023] QI0SSI in the link *L' may be represented as follow:
where,
T is the current across the link ;L,'
*Vd* is the voltage drop across the link ~L,'
"X' is the equivalent reactance on the link "L'

[0024] The existing approaches used Qioss as an indicator for a link to be weak. However, in such approaches. Qloss is dependent on current through the link and reactance across the link. Since these two parameters may not be available at the system 200, various embodiments consider a ratio of Q|0SSl by PL, (as given above in equation 1) for computing VS1L since this ratio may be obtained using only phasor values at the buses across a link. As given in equation 3, in order to eliminate the need for current T measurement across the link "L," the current T may be calculated as a ratio of the voltage drop 'Vd' across the link 'L' to the equivalent reactance *X' across the link 'L.' This equivalent reactance 'X' may include equivalent impedance value of the link 4L,' which may be a combination of resistance, inductive reactance, and capacitive reactance, in some embodiments, using equations 2 and 3 and replacing voltage drop 'V^ with a phasor voltage drop across the link *L' in the two-bus electrical system 300, Q,2 and Q2\ may be expressed as:

[0025] Applying these values for Q]2 and Q2I in equations 1 and 2, the ratio QioSSi by PLI may be calculated as follows:

[0026] Further, the power flow *PL1' across the link 4L' may be expressed as a function of the reactance ;X' across the link 'L,' the voltage magnitudes 'V,' and "VV at the respective buses 304 and 306, and phase angles 'Si* and '82,' at the respective buses 304 and 306. The power flow *PLl' may be expressed by any of the following equations:

[0027] In some embodiments, the ratio OH/PLI may be calculated from the equations 4, 7 and 8. This ratio may be expressed by any of the following equations:

[0028] Similarly, in some other embodiments, the ratio 02|/PLi may be calculated from the equations 5, 7 and 8. This ratio may be expressed by any of the following equations:

[0029] In various embodiments, as shown above in equations 7 and 8, the resistance (not shown) across the link 'L* may be neglected for the calculation of power flow *PL1' and 'Qiossi' since the resistance may be small compared to the reactance 'X' across the link 'L.' In order to eliminate reactance 'X,' VSI at the link *L' (VSILI) may be determined as the ratio of Qioss, and PL1. In some embodiments, using equations 1, 6 and 7, the 'VSILI' at the link 'V may be computed by:

[0030] Alternatively, in some other embodiments, using equations 1, 6 and 8, the 'VSILI' may be computed by:

[0031] In some embodiments, when an angular difference (that is, '53 - 81" or 'Si - 82') across the link 'L' is small, the denominator in equations 13 and 14 will tend to zero. However, the small angular difference may indicate a small link 'L* and therefore may not be useful for identification of weakest link or determination of voltage instability in the system 100.

[0032] Similar to the computation of VSIU corresponding to one link '1/ in the system 100. the computation module 216 may be configured to compute VSIs corresponding to other links in the system 100.

[0033] In some alternate embodiments, the computation module 216 may be configured to compute VSlL in the system 100 as a function of changes in reactive power losses (AQ]0SS) in the plurality of links, and changes in power flows (APL) across the plurality of links. In one exemplary embodiment, in order to compute VSI at the link 'L' (VSILI). a change in reactive power loss (AQtossl) in the link *L' and a change in power flow (APLi) across the link VL' may be determined. Referring to Fig. 3, these changes may be determined by measuring phasor values at the buses 304 and 306 at different time instances. In such an embodiment, phase angles '81-n' and *S2Ti' at respective buses 304 and 306, and voltage magnitudes *V1T1' and *V2Ti' at respective buses 304 and 306 may be measured at a time instance Tl;* and phase angles *51T2* and 'S2T2' at respective buses 304 and 306, and voltage magnitudes 'Vl-^7 and *V2T2' at respective buses 304 and 306 may be measured at a time instance *T2.* In some embodiments, the time instance *T2' may be greater than the time instance *T1.' Thereafter, in some embodiments, in order to compute VS1L], the computation module 216 may be configured to calculate change in reactive power loss (AQkwsi) in the link 'L' and change in power flow (APL,) across the link 'L,' as follow:
where,
QIOSSTI and QIOSST2 are reactive power losses in the link 'L* determined at time instances Ti' and 'T2,' respectively, and
PLTI and PLr2 are power flows across the link *L* determined at time instances 'Tl' and 'T2,* respectively

[0034] The above equation may be applicable only when PLT2 deviates from PLTI by about one percent or more.

[0035] Using equations 13 and 14, in some embodiments, VSIL, in the equation 15 may be computed as follows-.

[0036] In some embodiments, the utility operator may monitor the signs of numerator and denominator separately in the equation 15 to identify whether the reactive losses in the link 'L' or the system 100 are increasing or decreasing. In one embodiment, when both numerator and denominator are positive, the utility operator may infer that the reactive losses are increasing. In such embodiments, since the reactive losses are increasing, the utility operator may take appropriate actions to reduce losses, for example, decrease loads or provide reactive support, or reschedule power flow in the system 100. In alternate embodiment, when both numerator and denominator are negative, the utility operator may infer that the reactive losses are decreasing. In such embodiments, since the reactive losses are decreasing, the utility operator may configure the voltage stability determination module 236 to consider the VSIU as less critical (among VSIs with similar magnitudes) for the determination of voltage instability in the system 100. In one embodiment, the utility operator may use such information for any other purpose.

[0037] In some embodiments, the utility operator may also monitor the difference between QIOSST2 and Qi0SsTi by observing the value of numerator in the equation 15. Significant increase or decrease (may be defined by the utility operator) in reactive power loss at time 'T2' (QiossT1) with respect to Q]ossTi may be due to switching of reactive power support at one or more buses in the system 100 or due to change in a transformer tap position, in accordance with some embodiments. In such embodiments or even otherwise, the utility operator may further monitor reactive power losses in the link ;L,' for example, at time instances 'T3,' *T4* and so on, to check whether the significant increase or decrease in the reactive power loss is damped to a value closer to QiossT- In one embodiment, if the reactive power loss is damped, then the utility operator may consider the VSIU as less critical (among VSIs with similar magnitudes) for the determination of voltage instability in the system 100 since the significant increase or decrease may be due to switching of reactive power support or change in a transformer tap position.

[0038] Further, in some embodiments, in order to determine voltage instability in the system, the utility operator may define or dynamically compute a threshold value (for example, one or two) for comparison with VSILI (and VSIs for other links) computed using equation 15. In some other embodiments, multiple threshold values may be defined or dynamically computed. The voltage stability determination module 236 may be configured to determine voltage instability in the system 100 if any of the VSIL computed using equation 15 is equal to or greater than this threshold value(s), in accordance with various embodiments.

[0039] Alternatively, in some other embodiments, the computation module 216 may be configured to compute VS1L in the system 100 as a function of rates of change in reactive power losses in the plurality of links, and rates of change in power flows across the plurality of links.

[0040] In some embodiments, multiple phasor values may be obtained for each bus in the system 100 and these phasor values may be processed by the processor 206 prior to the computation of VSIL at the plurality of links in the system 100. In one exemplary embodiment, sixty samples of phasor values may be measured or obtained every second for each bus in the system 100. In such an embodiment, few samples (for example, 2-10 samples) for a bus may have phasor values that may be significantly different from other samples for the same bus. The significant difference in few samples may be due to changes in the power quantities in the system 100 or due to some error in the measurement. In some embodiments, in order to eliminate any inaccuracy in the computation of VSIL. an average of the samples of phasor values, measured or obtained over a time period (for example, one second) for each bus in the system 100, may be calculated. Such averages may then be used to compute VSIL in the system 100. In some alternate embodiments, any other technique may be used to compensate for inaccuracy in the computation of VSIL, which may result in inaccuracy in the identification of weak buses in the system and false alarming of voltage instability in the system 100. In one example, an integration of the samples measured or obtained over a time period (for example, every second) for each bus in the system 100 may be used for computation of VSU.. In another example, an existing filtering device may be used to remove few samples (for example, 2-10 samples from a total of 60 samples) that are significantly different from other samples being measured or estimated for the same bus over a certain time period.

[0041] Referring back to Fig. 2, in some embodiments, once the phasor values are measured or estimated, and VSIL computed, a location identification module 218 in the processor 206 may be configured to analyze VSIL computed by the computation module 216. In one embodiment, the location identification module 218 may be configured to identify weak links from the plurality of links based on VSIL. In one exemplary embodiment, the location identification module 218 may be configured to identify weak links by determining a maximum value from the computed VS1L and then by defining a link having this maximum value as the weakest link. This maximum value is hereinafter referred to as maximum link VS1 (VSILmav). In an alternate embodiment, the computation module 216 (instead of the location identification module 218) may be configured to determine this VSlLmax. Thereafter, in such an embodiment, the location identification module 218 may be configured to define the link having this VSILmBX as the weakest link.

[0042] VSILIMX may not always signify the weakest link in the system 100 since the VSILmav may have a lower value indicating that the link with VSILma* is still a stronger link in the system 100, even though it may be weaker with respect to other links in the system 100. In order to handle such scenarios, in some embodiments, the location identification module 218 may be configured to identify weak links in the system 100 by comparing the computed VS1L with one or more weak link threshold values (hereinafter referred to as 'weak link threshold values'). In such embodiments, if this comparison results in any or some of the computed VS1L being greater than or equal to the weak link threshold values, the location identification module 218 may be configured to define the links having such VSIs as weak links in the system 100. In some other embodiments, the location identification module 218 may be configured to compare only VSILmax (from the computed VSIL) with the weak link threshold values to identity a weakest link in the system 100. In such embodiments, if this comparison results in VSILmax being greater than or equal to the weak link threshold values, the location identification module 218 may be configured to define the link having VSILmax as the weakest link in the system 100.

[0043] In some embodiments, the weak link threshold values may be defined or modified by the utility operator (or protection engineer), or dynamically defined and controlled. In one embodiment, each weak link threshold value may be meant to provide an indicator to the utility operator or the protection engineer. In one exemplary embodiment, one weak link threshold value (for example, between 0.71 to 0.8) may be meant to provide a warning or an alert to the utility operator that one or more links with VSIs (or VSlLmm) greater than or equal to this threshold value may be approaching a threshold value (hereinafter referred to as "link stability threshold value') associated with a critical point in the system 100. Critical point is a point at which the system 100 may undergo a phase transition, for example, become voltage unstable and thus the system 100 may collapse. In another exemplary embodiment, another weak link threshold value (for example, between 0.81 to 0.9) may be meant to provide an emergency indicator to the utility operator that one or more links with VSIs (or VSILmax) greater than or equal to this threshold value may be approaching the voltage instability and hence the utility operator may generate a control action to ensure that such VSIs are maintained below the link stability threshold value. The control action may include, but not limited to, enhancement of reactive power support, load shedding, or system re-configuration.

[0044] Further, in some embodiments, the location identification module 218 may be configured to generate a notification message to indicate one or more categories of the weak links to the utility operator. The "categories of the weak links' as used herein are defined based on the type of weak link threshold values. For example, a link 'LT may have a VS1 value that may be greater than or equal to a weak link threshold value that is meant to provide a warning or an alert but less than a weak link threshold value that is meant to provide an emergency indicator. This link may be categorized into category 'A' of weak links. On the other hand, in another example, a link 'L2' may have a VS1 value that may be greater than or equal to a weak link threshold value that is meant to provide an emergency indicator. This link may be categorized into category 'B' of weak links. In one exemplary embodiment, the notification message may be an audio or a visual indicator to the utility operator that the system 100 is approaching the voltage unstable condition.

[0045] Various embodiments explained herein (such as, for the computation of VSIL, defining of one or more weak links, and so on) may be implemented when the computation of two or more VSIs (VSlbus) corresponding to two or more buses in the system 100 results in such VSlbus having same value. In such embodiments, the weaker bus from these two or more buses in the system 100 may be determined based on the weak links in the system 100. Various techniques described above for determining weak links may be used in such embodiments to determine which link of these links is weak link. VSIbus may be computed using any existing approach that is used for the computation of VSIs for buses in an electrical power system. In some embodiments, one or more links may be electrically isolated from the system 100 to avoid or eliminate any unwanted and uncontrollable collapses, or costlier counter measures, upon determining that VSIs for one or more links in the system 100 are greater than or equal to the link stability threshold value.

[0046] Connectivity information including configuration of buses and links in the system 100 may be required to identify which buses (and their corresponding phasor values) connected to the corresponding link (determined from the connectivity information) need to be considered for computing VSI[,, in accordance with some embodiments. In some other embodiments when the phasor values measured at a current time instance TT signify significant change in these measured values with respect to those measured at an earlier time instance "T2,' a status (for example. OFF or ON) of a circuit breaker associated with a link 'LI' (that is normally connecting two buses at its two respective ends) may be identified in order to determine whether a link is electrically disconnected from buses at which the phasor values are measured. For example, when the phase angle or voltage magnitude measured at the time instance "TV shows a variation of about, for example, twenty percent or more than the phase angle or voltage magnitude measured at the earlier time instance *T2,* then the status of the circuit breaker may be identified. In this example, an OFF status of the circuit breaker may signify that the link 'LI' may be electrically disconnected from buses at which the phasor values are measured at time instances 'TT and 'T2.' In such an example, the utility operator may monitor the connectivity information to check whether these buses are connected via a different link due to which the phasor values have changed significantly. In such a case, the utility operator may decide to use the phasor values measured for these buses to check whether this (different) link is weak.

[0047] In various embodiments, the directions of reactive power flow in the links with respect to (real) power flow across these links in the system 100 may be used to determine which of these links are weaker than the other links in the system 100. These directions may be used when the computation of VSIL in the system 100 results in some of these VSIL having same value. The directions may help in determining the type of compensation and overall reactive power loss for a particular link, which in turn may signify the criticality (or weakness) of that link. In one embodiment, as shown in Fig. 3, if Si is greater than 52, the direction of the power flow Pu may be from the bus 304 to the bus 306. However, in one such embodiment as shown in Fig. 3, the directions of the reactive power flows Q,2 and Q2i may be inward from the respective buses 304 and 306 toward the link 'L.* In such embodiments, the overall Q!ossl may be more with respect to overall reactive power loss in the same link where the direction of Ql2 is outward from the link *L' toward the bus 304 and the direction of Q2, may be inward from the bus 306 toward the link 'L.' In the latter case, even though the system 100 may be over-compensated, the overall reactive power loss will be less as compared to the former case. In another embodiment, when the direction of Ql2 may be inward from the bus 304 toward the link 'L' and the direction of Q21 may be outward from the link 4L' toward the bus 306, the system 100 may be under-compensated and the overall Q,ossl may be more with respect to overall reactive power loss in the same link where the directions of both On and O21 are outward from the link 'L' toward the respective buses 304 and 306. In the latter case, even though the system 100 may be under-compensated, the overall reactive power loss will be less as compared to the former case. Since links with higher reactive power losses are weak links, the link 'V as shown in Fig. 3 and another link 'LT (not shown) where the direction of Ql2 may be inward from the bus 304 toward that link 'LP and the direction of Q,i may be outward from the link 'LV toward the bus 306 may be defined as weak links in the system 100 as these links are critical for determining voltage instability in the system 100.

[0048] It will be apparent to a person skilled in the art that if the direction of the power flow Pu is reversed (that is, from the bus 306 to the bus 304). then the directions of Ql2 and Q2i will be accordingly reversed and hence the compensation will be determined accordingly.

[0049] In some embodiments, the local or remote workstation 214 may be configured to communicate with the location identification module 218 either via the communication network 212 or directly as shown in Fig. 2. In such embodiments, the location identification module 218 may be configured to identify locations of weak links in the system (such as 100) by generating location information of the weak links, for example, location identities (IDs) corresponding to the weak links. The location identification module 218 may be further configured to transmit this location information to the local or remote workstation 214 for notifying the location of the weak links in the system (such as 100) to the utility operator or protection engineer. In one exemplary embodiment, the utility operator or protection engineer may, for example, view these locations on a display (not shown) provided at the local or remote workstation 214. In some embodiments, the local or remote workstation 214 may be implemented in the system 200 or anywhere in an electrical power system (such as 100).

[0050] Further, in some embodiments, once the weak links are determined in the system 100, voltage instability in the system 100 may be determined. The processor 206 may include a voltage stability determination module 236 that may be configured to determine voltage instability in the system 100 based on the link stability threshold value. In some embodiments, this threshold value may be same or different from one of the weak link threshold values. In one exemplary embodiment, the voltage stability determination module 236 may be configured to compare the determined VSILmax with the link stability threshold value. In one such embodiment, the voltage stability determination module 236 may be configured to determine voltage instability in the system 100 if the VSILmas is greater than or equal to the link stability threshold value.

[0051] The link stability threshold value at which the system 100 may collapse due to voltage instability may depend on the reactive power support provided in the system 100, in accordance with some embodiments. In one exemplary embodiment, a reactive power support (for example, generator 'G2' as shown in Fig. 3) at the load-end of the system 100 may regulate the voltage magnitudes at the load-end to about one pu. In such an embodiment when the link 'L' is over-compensated by providing infinite reactive power support at both source and load ends, VSlLmax may approach two as indicated in the equation 16 below. This value is the link stability threshold value for over-compensated systems and may indicate the steady state maximum loading that can be achieved on a link. In such a condition, voltage magnitudes (V, and V2) at both source and load ends may be one. The maximum power transfer in such an embodiment may be constrained by 8 equal to 90 degrees (or about 1.6 radians). Referring back to Fig. 3, under such operating condition and using equations 3 and 13, VSILinas of the link 'L1 may be calculated by:

[0052] In another exemplary embodiment, for under-compensated system, the link stability threshold value may be about one.

[0053] As explained above, over-compensation and under-compensation may be determined based on the directions of Q]2 and Q2] in a link in the system 100. The link stability threshold value and the weak link threshold values may be different for different levels of compensation. In one exemplary embodiment, for over-compensated systems, when the link stability threshold value is 2, the weak link threshold values may be, for example, between 1.6 to 2. In another exemplary embodiment, for under¬compensated systems, when the link stability threshold value is 1, the weak link threshold values may be, for example, between 0.7 to 0.9. Firstly, VSILmaxh or VSls greater than or equal to first weak link threshold values (defined for over-compensated system), may be computed from VSIs of the over-compensated links for identification of a first set of weak links. Secondly, VSILmax2, or VSIs greater than or equal to second weak link threshold values (defined for under-compensated system), may be computed from VSIs of the under-compensated links for identification of a second set of weak links.

[0054] As described above, in some exemplary embodiments, the link stability threshold value may be two for over-compensated links and one for under-compensated links. In some embodiments, similar to the identification of weak links for under¬compensated and over-compensated systems, voltage instability in the system 100 may be determined by comparing VSILmaxi of the over-compensated weak link with one link stability threshold value (for example, 2) for the over-compensated system, and by comparing VSlLmax2 of the under-compensated weak link with another link stability threshold value (for example, 3) for the under-compensated system. In such embodiments, the voltage stability determination module 236 may be configured to determine voltage instability in the system 100 if any one of, or both. VSI|_„,axi and VSILmax2 are greater than or equal to respective link stability threshold values.

[0055] In some alternate embodiments, VSIuTi and VSILma.2 may be normalized (using a normalization factor) to compare with a single link stability threshold value, or a common weak link threshold value (instead of first and second weak link threshold values), or both for over-compensated and under-compensated weak links. Similarly, in some other embodiments, VSIs computed separately for over-compensated and under-compensated weak links may be normalized for comparing these computed VSIs with a common weak link threshold value (instead of first and second weak link threshold values) for over-compensated and under-compensated weak links. In one exemplary embodiment, in order to normalize for different threshold values for over-compensated and under-compensated weak links, the below equation n.ay be used to compute VSILI.
where, "Min {2, [2 - (Q21/Q12)]}' is a normalization factor and signifies that the minimum value of 2 and the resultant value of '[2 - (Qiv'QnW ™ay be used as the normalization factor and then this normalization factor may be multiplied to the ratio to obtain VSIL1.

[0056] The above equation 17 may be applicable only when Q12 is greater than zero. In equation 17, the ratio Qi0SSi/PLi may be computed using the equation 13 or 14. Similarly, Q,2 may be computed using the equation 9 or 10, and Q2i may be computed using the equation 11 or 12.

[0057] In some embodiments, the magnitude of O2] may be used to determine the level of compensation, that is, how much active or reactive compensation is provided to a particular link. For example, for Q2, less than or equal to zero, the link 'L' may be under-compensated; whereas for Q2i greater than zero, the link *L' may be over-compensated. For over-compensated links, the links with greater value of Q2\ may be considered more compensated than the links with comparatively lesser value of Q2\- 1° one embodiment, the link 'L? may be fully compensated if the ratio Q2]/Qi2 is one, that is, when Q12 and Q2] are same.

[0058] Similar to VS1L1 that is computed for the link "L,' VSIs for other links may be computed using an equation similar to the equation 17. Once these VSIs are computed, any technique described above in various embodiments for identifying weak links and determining voltage instability may be used for identification of weak links and determination of voltage instability in the system 100.

[0059] Any other normalization technique may be used herein without deviating from the scope of the invention. In one exemplary embodiment, voltage magnitudes determined at the buses (connecting a link) may be used, instead of Q[2 and Q2,, for the identification of the level of compensation, or for computing the normalization factor, or both.

[0060] Alternatively, in another exemplary embodiment, the link stability threshold value may be determined using any other technique. For example, an electrical operator may define this threshold value for over-compensated electrical power system. In another example, this threshold value may be dynamically derived, for example, from power system quantities such as reactive power.

[0061] Figs. 2 and 3 above consider the embodiments where a single control center system 200 exchanges data directly with the monitoring modules 126. However, in some other embodiments, multiple control center systems may be used without deviating from the scope of the invention.

[0062] In one embodiment, a method for identification of weak links is presented. Fig. 4 is a flowchart depicting a method 400 for identification of weak links from a plurality of links and determination of voltage instability in an electrical power system (such as 100), in accordance with one embodiment. At step 402, phasor values associated with a plurality of buses ('m' buses) may be determined. In one exemplary embodiment, a phasor measurement unit (PMU) or a relay embedding functionalities of PMU may be used to determine these phasor values. In another exemplary embodiment, the phasor values may be obtained from, but not limited to, an energy management system (EMS), a manual input from a utility operator, historical data of the phasor values, or a tool for computing the phasor values, or any combination thereof.

[0063] At step 404, VSIs (VS1;.) corresponding to plurality of links in the electrical power system may be computed as a function of phasor values at the 'm' buses. In one embodiment, a phasor value at an 'mnY bus may include voltage magnitude (Vm) and phase angle (8m). both corresponding to the same *mth* bus. Various embodiments described above in conjunction with Figs. 1-3 may be equally applied to the method 400 for the computation of VSIL.

[0064] Further, at step 406, weak links may be identified from the plurality of links in the electrical power system based on the computed VSIL. In one embodiment, the weak links may be identified by determining a maximum VSI (VSILmax) from the computed VSIL, and then defining the link with VSILma* as the weakest link. In another embodiment, weak links in the system may be identified by comparing the computed VSIL with weak link threshold values. In such embodiments, if this comparison results in any or some of the computed VSIL being greater than or equal to the weak link threshold values, the links having such VSIs may be defined as weak links in the system. Alternatively, in another embodiment, only VSILmax (from the computed VSIL) may be compared with the weak link threshold values to identify a weakest link in the system.

[0065] In some embodiments, once the weak links are determined in the electrical power system (such as 100), the method 600 may further determine voltage instability in the system based on a link stability threshold value. In one exemplary embodiment, VSlLma)L may be compared with this threshold value. In such an embodiment, the voltage instability in the system is determined if VSI[max is greater than or equal to this threshold value.

[0066] Various embodiments described above in conjunction with Figs. 1-3 above may be equally applied to the method 400 for the identification of weak links and determination of voltage instability in the electrical power system (such as 100).

[0067] The systems and methods in accordance with embodiments of the invention may provide determination of weak links or a weakest link in an electrical power system (such as 100) in real-time. Embodiments of the system and method disclosed herein may ensure that determining the weak links or weakest link may be used to implement appropriate counter-measures to reduce or eliminate any damage and prevent cascading effects caused due to delay in the detection of voltage instability. Various embodiments disclosed herein may implement counter-measures when the comparison of maximum VSI (VSI[max) with a link stability threshold value indicates voltage instability in the system. Various embodiments avoid delay in the detection of voltage instability by using phasor values to compute VSIL and by determining weak links or voltage instability in the system based on these computed VSIL.. By using only phasor values, various embodiments further eliminate the need for any additional information such as current magnitude, network parameters, loading condition, changes in controls, outages, and so on for the computation of VSIL and determination of weak links or voltage instability in the system.

[0068] Various embodiments may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment containing both hardware and software components. In accordance with one embodiment, the invention may be implemented in software, which includes but is not limited to firmware, resident software, or microcode.

[0069] The skilled artisan will recognize the interchangeability of various features from different embodiments. Similarly, the various method steps and features described, as well as other known equivalents for each such methods and features, can be mixed and matched by one of ordinary skill in this art to construct additional assemblies and techniques in accordance with principles of this invention. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.

CLAIMS

1. A method, comprising:
(i) computing voltage stability indices (VS1L) corresponding to a plurality of links in an electrical power system as a function of phasor values associated with a plurality of buses, wherein each of the phasor values comprising voltage magnitude (Vm) corresponding to the respective bus, and phase angle (8m) corresponding to the respective bus; and

(ii) identifying one or more weak links from the plurality of links in the electrical power system based on the computed VSIL-

2. The method of claim 1, wherein the step (i) comprises computing a VSI (VS1U) corresponding to a link (L) from the plurality of links as a function of phasor values associated with a pair of buses connected by the link (L), wherein the pair of buses includes two buses of the plurality of buses.

3. The method of claim 1, wherein the step (i) comprises computing the VS1L corresponding to the plurality of links as a function of reactive power losses (Qioss) in the plurality of links and power flows (PL) across the respective plurality of links.

4. The method of claim 1, wherein the step (i) comprises computing the VSIL corresponding to the plurality of links as a function of:
changes in reactive power losses (AQioss) or rates of change of reactive power losses in the plurality of links, and

changes in power flows (APL) or rates of change of power flows across the plurality of links.

5. The method of claim 1, further comprising determining a maximum link VSI (VSILmax) corresponding to a respective link from the computed VSIL..

6. The method of claim 5, wherein the step (ii) comprises defining the link with the maximum link VSI (VSILmax) as the one or more weak links.

7. The method of claim 5, further comprising:

comparing the maximum link VSI (VSILmax) with a link stability threshold value; and

determining voltage instability in the electrical power system if the maximum link VSI (VSli.max) is greater than or equal to the link stability threshold value.

8. The method of claim 1,wherein the step (i) comprises computing the VSILas a function of a normalization factor.

9. The method of claim 1, further comprising:

comparing one of: the computed VSIL, or a maximum link VSI (VSILmax) from the computed VSI, with one or more weak link threshold values;

determining one or more VSIs from the computed VSIL, or the maximum link VSI (VSlLmax), as greater than or equal to the weak link threshold values based on the comparison; and

defining one or more links, corresponding to one of: the one or more VSIs or the maximum link VSI (VSILma), as the one or more weak links.

10. The method of claim 9, further comprising generating a notification message to indicate one or more categories of the one or more weak links.

11. A system, comprising:
an computation module configured to compute voltage stability indices (VSIL) corresponding to a plurality of links in an electrical power system as a function of phasor values associated with a plurality of buses, wherein each of the phasor values comprising voltage magnitude (Vm) corresponding to the respective bus. and phase angle (5in) corresponding to the respective bus; and

a location identification module configured to identify one or more weak links from the plurality of links in the electrical power system based on the computed VSIL.

12. The system of claim 11, wherein the computation module is configured to compute a VSI (VSILi) corresponding to a link (L) from the plurality of links as a function of phasor values associated with a pair of buses connected by the link (L), wherein the pair of buses includes two buses of the plurality of buses.

13. The system of claim 11, wherein the computation module is configured to compute the VSIL corresponding to the plurality of links as a function of reactive power losses (Qioss) '" the plurality of links and power flows (PL) across the respective plurality of links.

14. The system of claim 11, wherein the computation module is configured to compute the VS1L corresponding to the plurality of links as a function of:

changes in reactive power losses {AQ(os;;) or rates of change of reactive power losses in the plurality of links, and

changes in power flows (APL) or rates of change of power flows across the plurality of links.

15. The method of claim 11, wherein one of the computation module or the location identification module is configured to determine a maximum link VSI (VSILniax) corresponding to a respective link from the computed VS1L.

16. The system of claim 15, wherein the location identification module is configured to define the link with the maximum link VSI (VSlLmax) as the one or more weak links.

17. The system of claim 15. further comprising a voltage stability determination module configured to:

compare the maximum link VSI (VSILmax) with a link stability threshold value, and

determine voltage instability in the electrical power system if the maximum link VSI (VSILma.O is greater than or equal to the link stability threshold value.

18. The system of claim 11. wherein the computation module is further configured to obtain the phasor values using at least one of: one or more phasor measurement units (PMUs) monitoring the plurality of buses, an energy management system (EMS), a manual input from a utility operator, historical data of the phasor values, or a tool for computing the phasor values.

19. The system of claim 11, wherein the location identification module is further configured to:

compare one of: the computed VS1L, or a maximum link VSI (VSILnm) from the computed VSIL with one or more weak link threshold values,

determine one or more VSls from the computed VSIL, or the maximum link VSI (VSlLmax), as greater than or equal to the weak link threshold values based on the comparison, and

define one or more links, corresponding to one of: the one or more VSls or the maximum link VSI (VSILmax), as the one or more weak links.

20. The system of claim 19, wherein the location identification module is further configured to generate a notification message to indicate one or more categories of the one or more weak links.