Patent Publication Number: US-10310480-B2

Title: Systems and methods for under-frequency blackout protection

Description:
RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. Non-Provisional patent application Ser. No. 13/195,227, filed 1 Aug. 2011, titled “SYSTEMS AND METHODS FOR UNDER-FREQUENCY BLACKOUT PROTECTION”, which claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 61/376,348, filed Aug. 24, 2010, titled “WIDE AREA UNDER-FREQUENCY BLACKOUT PROTECTION SYSTEM,” which are hereby incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to systems and methods for controlling and protecting an electric power delivery system and, more particularly, to systems and methods for wide-area under-frequency blackout protection in an electric power delivery system using rotor angles of synchronous machines. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Non-limiting and non-exhaustive embodiments of the disclosure are described, including various embodiments of the disclosure, with reference to the figures, in which: 
         FIG. 1  illustrates a simplified diagram of one embodiment of an electric power delivery system that includes intelligent electronic devices. 
         FIG. 2  illustrates a block diagram of one embodiment of an intelligent electronic device for protection and control of an electric power delivery system. 
         FIG. 3  illustrates another block of one embodiment of an intelligent electronic device for protection and control of an electric power delivery system. 
         FIG. 4  illustrates one embodiment of a method for protection and control of an electric power delivery system. 
         FIG. 5A  illustrates a conceptual diagram of a rotor of a synchronous generator consistent with embodiments disclosed herein. 
         FIG. 5B  illustrates a conceptual diagram of the rotor illustrated in  FIG. 5A  and a stator, which together may operate as a synchronous generator. 
         FIG. 6  illustrates a power angle curve for an exemplary power generator. 
         FIG. 7  illustrates a simplified partial cross-sectional view of a magnetic pickup unit (MPU) consistent with embodiments disclosed herein. 
         FIG. 8  illustrates another block diagram of one embodiment of an intelligent electronic device for protection and control of an electric power delivery system. 
         FIG. 9  illustrates a simplified diagram of one embodiment of an electric power delivery system that includes intelligent electronic devices. 
     
    
    
     DETAILED DESCRIPTION 
     The embodiments of the disclosure will be best understood by reference to the drawings. It will be readily understood that the components of the disclosed embodiments, as generally described and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the systems and methods of the disclosure is not intended to limit the scope of the disclosure, as claimed, but is merely representative of possible embodiments of the disclosure. In addition, the steps of a method do not necessarily need to be executed in any specific order, or even sequentially, nor do the steps need be executed only once, unless otherwise specified. 
     In some cases, well-known features, structures, or operations are not shown or described in detail. Furthermore, the described features, structures, or operations may be combined in any suitable manner in one or more embodiments. It will also be readily understood that the components of the embodiments, as generally described and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations. For example, throughout this specification, any reference to “one embodiment,” “an embodiment,” or “the embodiment” means that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment. Thus, the quoted phrases, or variations thereof, as recited throughout this specification are not necessarily all referring to the same embodiment. 
     Several aspects of the embodiments described are illustrated as software modules or components. As used herein, a software module or component may include any type of computer instruction or computer executable code located within a memory device that is operable in conjunction with appropriate hardware to implement the programmed instructions. A software module or component may, for instance, comprise one or more physical or logical blocks of computer instructions, which may be organized as a routine, program, object, component, data structure, etc., that performs one or more tasks or implements particular abstract data types. 
     In certain embodiments, a particular software module or component may comprise disparate instructions stored in different locations of a memory device, which together implement the described functionality of the module. Indeed, a module or component may comprise a single instruction or many instructions, and may be distributed over several different code segments, among different programs, and across several memory devices. Some embodiments may be practiced in a distributed computing environment where tasks are performed by a remote processing device linked through a communications network. In a distributed computing environment, software modules or components may be located in local and/or remote memory storage devices. In addition, data being tied or rendered together in a database record may be resident in the same memory device, or across several memory devices, and may be linked together in fields of a record in a database across a network. 
     Embodiments may be provided as a computer program product including a non-transitory machine-readable medium having stored thereon instructions that may be used to program a computer or other electronic device to perform processes described herein. The non-transitory machine-readable medium may include, but is not limited to, hard drives, floppy diskettes, optical disks, CD-ROMs, DVD-ROMs, ROMs, RAMs, EPROMs, EEPROMs, magnetic or optical cards, solid-state memory devices, or other types of media/machine-readable medium suitable for storing electronic instructions. In some embodiments, the computer or other electronic device may include a processing device such as a microprocessor, microcontroller, logic circuitry, or the like. The processing device may further include one or more special purpose processing devices such as an application specific interface circuit (ASIC), PAL, PLA, PLD, field programmable gate array (FPGA), or any other customizable or programmable device. 
     Electrical power generation and delivery systems are designed to generate, transmit, and distribute electrical energy to loads. Electrical power generation and delivery systems may include equipment, such as electrical generators, electrical motors, power transformers, power transmission and distribution lines, circuit breakers, switches, buses, transmission lines, voltage regulators, capacitor banks, and the like. Such equipment may be monitored, controlled, automated, and/or protected using intelligent electronic devices (IEDs) that receive electric power system information from the equipment, make decisions based on the information, and provide monitoring, control, protection, and/or automation outputs to the equipment. 
     In some embodiments, an IED may include, for example, remote terminal units, differential relays, distance relays, directional relays, feeder relays, overcurrent relays, voltage regulator controls, voltage relays, breaker failure relays, generator relays, motor relays, automation controllers, bay controllers, meters, recloser controls, communication processors, computing platforms, programmable logic controllers (PLCs), programmable automation controllers, input and output modules, governors, exciters, statcom controllers, SVC controllers, OLTC controllers, and the like. Further, in some embodiments, IEDs may be communicatively connected via a network that includes, for example, multiplexers, routers, hubs, gateways, firewalls, and/or switches to facilitate communications on the networks, each of which may also function as an IED. Networking and communication devices may also be integrated into an IED and/or be in communication with an IED. As used herein, an IED may include a single discrete IED or a system of multiple IEDs operating together. 
     Electrical power generation and delivery system equipment may be monitored and protected from various malfunctions and/or conditions using one or more IEDs. For example, an IED may be configured to protect the electrical power system equipment from abnormal conditions, such as when the power generation capabilities of the electrical power system cannot adequately supply system loads. Under this unbalanced system condition, power loss or blackouts may occur that negatively affect both providers of electric power and their customers. Consistent with embodiments disclosed herein, an IED may utilize under-frequency (UF) load shedding techniques to minimize blackout conditions on a larger portion of the electric power delivery system. 
     Power imbalances in an electrical power delivery system may be associated with a fall in the frequency of the electrical power system fundamental voltage. Consistent with embodiments disclosed herein, when a threshold UF level is crossed, loads may be disconnected (e.g., shedded) from the electrical power system to rebalance the system. By shedding selective loads and rebalancing the system, the negative effects of unbalanced system conditions may be mitigated. 
       FIG. 1  illustrates a simplified diagram of an electric power generation and delivery system  100  that includes IEDs  102 - 108  consistent with embodiments disclosed herein. Although illustrated as a one-line diagram for purposes of simplicity, electrical power generation and delivery system  100  may also be configured as a three phase power system. Moreover, embodiments disclosed herein may be utilized any electric power generation and delivery system and is therefore not limited to the specific system  100  illustrated in  FIG. 1 . Accordingly, embodiments may be integrated, for example, in industrial plant power generation and delivery systems, deep-water vessel power generation and delivery systems, ship power generation and delivery systems, distributed generation power generation and delivery systems, and utility electric power generation and delivery systems. 
     The electric power generation and delivery system  100  may include generation, transmission, distribution, and power consumption equipment. For example, the system  100  may include one or more generators  110 - 116  that, in some embodiments, may be operated by a utility provider for generation of electrical power for the system  100 . Generators  110  and  112  may be coupled to a first transmission bus  118  via step up transformers  120  and  122 , which are respectively configured to step up the voltages provided to first transmission bus  118 . A transmission line  124  may be coupled between the first transmission bus  118  and a second transmission bus  126 . Another generator  114  may be coupled to the second transmission bus  126  via step up transformer  128  which is configured to step up the voltage provided to the second transmission bus  126 . 
     A step down transformer  130  may be coupled between the second transmission bus  126  and a distribution bus  132  configured to step down the voltage provided by the second transmission bus  126  at transmission levels to lower distribution levels at the distribution bus  132 . One or more feeders  134 ,  136  may draw power from the distribution bus  132 . The feeders  134 ,  136  may distribute electric power to one or more loads  138 ,  140 . In some embodiments, the electric power delivered to the loads  138 ,  140  may be further stepped down from distribution levels to load levels via step down transformers  142  and  144 , respectively. 
     Feeder  134  may feed electric power from the distribution bus  132  to a distribution site  146  (e.g., a refinery, smelter, paper production mill, or the like). Feeder  134  may be coupled to a distribution site bus  148 . The distribution site  146  may also include a distributed generator  116  configured to provide power to the distribution site bus  148  at an appropriate level via transformer  150 . In some embodiments, the distributed generator  116  may comprise a turbine configured to produce electric power from the burning of waste, the use of waste heat, or the like. The distribution site  146  may further include one or more loads  138 . In some embodiments, the power provided to the loads  138  from the distribution site bus  148  may be stepped up or stepped down to an appropriate level via transformer  142 . In certain embodiments, the distribution site  146  may be capable of providing sufficient power to loads  138  independently by the distributed generator  116 , may utilize power from generators  110 - 114 , or my utilize both the distributed generator  116  and one or more of generators  110 - 114  to provide electric power to the loads. 
     IEDs  102 - 108  may be configured to control, monitor, protect, and/or automate the electric power system  100 . As used herein, an IED may refer to any microprocessor-based device that monitors, controls, automates, and/or protects monitored equipment within an electric power system. An IED may include, for example, remote terminal units, differential relays, distance relays, directional relays, feeder relays, overcurrent relays, voltage regulator controls, voltage relays, breaker failure relays, generator relays, motor relays, automation controllers, bay controllers, meters, recloser controls, communications processors, computing platforms, programmable logic controllers (PLCs), programmable automation controllers, input and output modules, motor drives, and the like. In some embodiments, IEDs  102 - 108  may gather status information from one or more pieces of monitored equipment. Further, IEDs  102 - 108  may receive information concerning monitored equipment using sensors, transducers, actuators, and the like. Although  FIG. 1  illustrates separate IEDs monitoring a signal (e.g., IED  104 ) and controlling a breaker (e.g., IED  108 ), these capabilities may be combined into a single IED. 
       FIG. 1  illustrates various IEDs  102 - 108  performing various functions for illustrative purposes and does not imply any specific arrangements or functions required of any particular IED. In some embodiments, IEDs  102 - 108  may be configured to monitor and communicate information, such as voltages, currents, equipment status, temperature, frequency, pressure, density, infrared absorption, radio-frequency information, partial pressures, viscosity, speed, rotational velocity, mass, switch status, valve status, circuit breaker status, tap status, meter readings, and the like. Further, IEDs  102 - 108  may be configured to communicate calculations, such as phasors (which may or may not be synchronized as synchrophasors), events, fault distances, differentials, impedances, reactances, frequency, and the like. IEDs  102 - 108  may also communicate settings information, IED identification information, communications information, status information, alarm information, and the like. Information of the types listed above, or more generally, information about the status of monitored equipment, may be generally referred to herein as monitored system data. 
     In certain embodiments, IEDs  102 - 108  may issue control instructions to the monitored equipment in order to control various aspects relating to the monitored equipment. For example, an IED (e.g., IED  106 ) may be in communication with a circuit breaker (e.g., breaker  152 ), and may be capable of sending an instruction to open and/or close the circuit breaker, thus connecting or disconnecting a portion of a power system. In another example, an IED may be in communication with a recloser and capable of controlling reclosing operations. In another example, an IED may be in communication with a voltage regulator and capable of instructing the voltage regulator to tap up and/or down. Information of the types listed above, or more generally, information or instructions directing an IED or other device to perform a certain action, may be generally referred to as control instructions. 
     The distributed site  146  may include an IED  108  for monitoring, controlling, and protecting the equipment of the distributed site  146  (e.g., generator  116 , transformer  142 , etc.). IED  108  may receive monitored system data, including current signals via current transformer (CT)  154  and voltage signals via potential transformer (PT  156 ) from one or more locations (e.g., line  158 ) in the distribution site  146 . The IED  108  may further be in communication with a breaker  160  coupled between the feeder  134  and the distribution site bus  148 . In certain embodiments, the IED  108  may be configurable to cause the breaker  160  to disconnect the distribution site bus  148  from the distribution bus  132 , based on monitored system data received via CT  154  and PT  156 . 
     Feeder  136  may be communicatively coupled with an IED  106  configured to control a breaker  152  between the loads  140  and the distribution bus  132  based on monitored system data. In some embodiments, the power provided to the loads  140  from the distribution bus  132  may be stepped up or stepped down to an appropriate level via transformer  144 . Like the IED  108  of the distribution site  146 , monitored system data may be obtained by IED  106  using CTs and/or PTs (not shown). 
     Other IEDs (e.g., IED  104 ) may be configured to monitor, control, and/or protect the electric power generation and delivery system  100 . For example IED  104  may provide transformer and generator protection to the step-up transformer  120  and generator  110 . In some embodiments, IEDs  104 - 108  may be in communication with another IED  102 , which may be a central controller, synchrophasor vector processor, automation controller, programmable logic controller (PLC), real-time automation controller, Supervisory Control and Data Acquisition (SCADA) system, or the like. For example, in some embodiments, IED  102  may be a synchrophasor vector processor, as described in U.S. Patent Application Publication No. 2009/0088990, which is incorporated herein by reference in its entirety. In other embodiments, IED  102  may be a real-time automation controller, such as is described in U.S. Patent Application Publication No. 2009/0254655, which is incorporated herein by reference in its entirety. IED  102  may also be a PLC or any similar device capable of receiving communications from other IEDs and processing the communications there from. In certain embodiments, IEDs  104 - 108  may communicate with IED  170  directly or via a communications network (e.g., network  162 ). 
     The central IED  102  may communicate with other IEDs  104 - 108  to provide control and monitoring of the other IEDs  104 - 108  and the power generation and delivery system  100  as a whole. In some embodiments, IEDs  104 - 108  may be configured to generate monitored system data in the form of time-synchronized phasors (synchrophasors) of monitored currents and/or voltages. IEDs  104 - 108  may calculate synchrophasor data using a variety of methods including, for example, the methods described in U.S. Pat. Nos. 6,662,124, 6,845,333, and 7,480,580, which are herein incorporated by reference in their entireties. In some embodiments, synchrophasor measurements and communications may comply with the IEC C37.118 protocol. In certain embodiments, IEDs  102 - 108  may receive common time signals for synchronizing collected data (e.g., by applying time stamps for the like). Accordingly, IEDs  102 - 108  may receive common time signals from time references  164 - 170  respectively. In some embodiments, the common time signals may be provided using a GPS satellite (e.g., IRIG), a common radio signal such as WWV or WWVB, a network time signal such as IEEE 1588, or the like. 
     Consistent with embodiments disclosed herein, IEDs  102 - 108  may be configured to determine a power system operating frequency from monitored system data. The operating frequency of the power system may be determined using many methods including, for example, measuring time between zero-crossings of voltage and/or current, measuring positive-sequence phasor rotations, measuring time between period voltage and/or current peaks, and/or the like. IEDs  102 - 108  may be further configured to indicate when an operating frequency falls below a predetermined level. In certain embodiments, an IED may have a number of different UF levels and may indicate when an operating frequency falls below one or more of the UF levels. 
       FIG. 2  illustrates a block diagram of an IED  200  for protection and control of an electric power delivery system (e.g., system  100  illustrated in  FIG. 1 ). IED  200  may communicate with one or more IEDs  111  configured to provide indications of UF events (e.g., when system operating frequencies fall below one or more UF levels) to IED  200 . In some embodiments, IEDs  222  may receive monitored system data and, based on the monitored system data, provide indications of UF events such as when measured operating frequencies fall below one or more UF levels to the IED  200 . 
     In some embodiments, IEDs  222  may be programmed with a predetermined UF set point (e.g., level) and be configured to provide time synchronized indications of UF events to the IED  200 . In some embodiments, IEDs  222  may include one or more set points (e.g., levels) and be configured to provide time synchronized indications of UF events (e.g., when one or more of the set points are crossed) to the IED  200 . Further, in certain embodiments, IEDs  222  may indicate the UF set point (e.g., level) breached, a time indication of the UF event, the power consumed by a load associated with the IED, and/or synchrophasor data which may include a load angle. 
     Based on the UF event indications received from IEDs  222 , IED  200  may determine whether specific loads are exhibiting UF events and whether such loads can be disconnected (e.g., shed) to limit and/or avoid UF events and systems disturbances. This functionality may be achieved using one or more functional modules  202 - 220  included in the IED  200 . For example, indications of UF events (e.g., breached UF set points, time indications of UF events, power consumed by loads associated with the IEDs, and/or synchrophasor data) detected by IEDs  222  may be provided to a UF level array calculation module included in the IED  200 . In certain embodiments, UF level array calculation module  208  may be configured to order UF events and their associated information based on time stamps indicating when the UF events were received by their associated IEDs  222  (e.g., UF events may be ordered based on their time of occurrence). Information from the UF level array calculation module  208 , including one or more ordered UF events may be provided to a coinciding UF level event calculation module  206 . The UF level event calculation module  206  may be configured to determine whether the one or more UF events ordered by the UF level array calculation module  208  are associated with a larger system UF event based on the time stamps associated with the one or more UF events. For example, the UF level event calculation module  206  may determine that a particular set of UF events ordered by the UF level array calculation module  208  are associated with a larger system UF event based on their occurrence within a particular time period (e.g, a 10 ms period). Based on the UF events occurring within a particular time period, the UF level array calculation module  208  may determine that the loads associated with the UF events are associated with a power sub-grid experiencing a UF condition and provide this information to a load reduction calculation module  204 . 
     The IED  200  may also include a user adjustable parameter module  202  that, in some embodiments, includes parameters defining an amount of load to be shed for a particular UF-level. In some embodiments, the amount of load to be shed may be in the form of a power/frequency value (e.g., MW/Hz). Information regarding the amount of load to be shed for a particular UF-level may be provided to the load reduction calculation module  204 . The load reduction calculation module  204  may also utilize information regarding the UF events provided by the UF level array calculation module  208  and UF level event calculation module  206 , including time indications of UF events and indications of UF set points breached. Based on the information received by the load reduction calculation module  204 , the load reduction calculation module  204  may determine an amount of load to shed (e.g., the about of load to shed from the system measured in MW) based on the defined user parameters and the other received UF event information. 
     IEDs  222  may be further configured to monitor the power consumed by the loads they are associated with. Information regarding the power consumed by loads associated with the IEDs  222  may be monitored in terms of power (e.g., MW) or other coupled parameters such as current. For example, in reference to  FIG. 1 , IED  106  may be capable of monitoring the power consumed by loads  140 , and IED  108  may be capable of indicating the power presented consumed by the distributed site  146 . 
     Consistent with some embodiments, information regarding the power consumed by loads may be provided to a power array calculation module  212  included in the IED  200 . In some embodiments, the power array calculation module  212  may calculate a power consumption value for each load (e.g., by using parameters coupled to power consumption such as current). Further, the power array calculation module  212  may sort and/or order specific loads based on their associated power consumption. 
     The user adjustable parameter module  202  may include a parameter that includes a priority indication for loads associated with the IEDs  222 . For example, the priority indication may include a priority queue indicating the order in which loads should be shed from the system in the event of an UF condition. Accordingly, the priority indication may indicate certain loads (e.g., a hospital) that should stay connected to the system in the event of an UF condition. 
     The information generated by the power array calculation module  212  may be provided to a load shedding selection module  210  included in the IED  200  along with the priority indication provided by the user adjustable parameter module  202 . The load shedding selection module  210  may further receive information related to an amount of load to shed from the load reduction calculation module  204 . Based on the received information (e.g., the amount of load to shed, the priority of the loads, and the amount of power consumed by the loads), the load shedding selection module  210  may determine which loads should be shed to reduce the effects of the detected UF event in the system. That is, the load shedding selection module  210  may match the amount of power to shed with the power used by each of the loads, prioritized by the priority information, and determine which loads to shed. 
     In some embodiments, the IED  200  may include a load shedding control module  214  configured to receive an indication from the load shedding selection module  210  of which loads should be shed and provide a control signal to the IEDs  222  associated with the loads that should be shed directing the IEDs  222  to shed (e.g., disconnect) the relevant loads from the system. For example, in reference to  FIG. 1 , the load shedding selection module  210  may determine that loads  140  should be shed, and the load shedding control module  214  may direct the IED  106  associated with the loads  140  to trip breaker  152 , thereby disconnecting the loads from the system  100 . 
     Information regarding power sub-grids within a greater grid topology of an electric power delivery system may also be used by the IED  200  to calculate which loads should be shed in view of UF conditions. In this context, IEDs  222  may provide load angle information (e.g., synchrophasor information) to a phase angle array calculation module  220  included in the IED  200 . In an electric power generation and delivery system, equipment (e.g., loads) associated with a certain power sub-grid of the electric power generation and delivery system may experience similar frequency decay rates when the system experiences an UF condition. Similarly, equipment associated with different power sub-grids may experience different frequency decay rates when the system experiences an UF. 
     For example, in a system having two sub-grids within a greater grid topology of an electric power delivery system, the probability of both sub-grids experiencing the same frequency decay rate in a system UF condition is low. In certain conditions, the frequency in one sub-grid may increase while the frequency in the other sub-grid may decrease. Moreover, even in conditions where both sub-grids exhibit a decay in frequency, the frequency decays will likely reach set UF threshold levels at differing times. Based on the above, by analyzing the decay rates and times of loads within a system, the IED  200  may determine which loads are associated with a particular power sub-grid. For example, if certain loads exhibit similar frequency decay rates occurring at similar times (e.g., within a 2 ms period), the IED  200  may determine that the loads are associated with a particular power sub-grids. In some embodiments, IED  200  and its associated modules  202 - 220  may determine which loads are associated with a particular power sub-grid based on the methods described in U.S. Patent Application Publication No. 2009/0089608 which is herein incorporated by reference in its entirety. 
     To enable the IED  200  to determine which loads are associated with a particular power sub-grid, IEDs  222  may communicate time-synchronized load phase measurements to IED  200  using, for example, the IEC C38.118 protocol. Load angles measured by the IEDs  222  may be provided to the phase angle array calculation module  220  that, in some embodiments, may store such information. The phase angle array calculation module  220  may provide the measured load angles to a sub-grid detection module  218 . Based on the measured load angles, the sub-grid detection module  218  may determine whether loads associated with the IEDs  222  are associated with particular sub-grids. 
     Information regarding which loads are associated with particular sub-grids may be provided to a sub-grid and priority based load selection module  216 . The sub-grid and priority based load selection module  216  may also receive the parameter that includes a priority indication for loads associated with the IEDs  222  from the user adjustable parameter module  202 . Additionally, the sub-grid and priority based load selection module  216  may receive an indication of the amount of load to be shed from the load reduction calculation module  204 . 
     Based on the information related to which loads are associated with particular sub-grids, the priority information for the loads, and/or the amount of load to be shed, the sub-grid and priority based load selection module  216  may determine which loads should be shed by the system to reduce the effects of UF conditions. This information may provided by the sub-grid and priority based load selection module  216  to the load shedding control module  214 . The load shedding control module may then use this information in conjunction with the information received from the load shedding selection module to determine which loads should be shed and direct the appropriate IEDs  222  to shed the loads from the system. 
     In some embodiments, the modules  202 - 220  included in IED  200  may be implemented in a programmable IED system. For example, the functionality of IED  200  may be achieved using a synchrophasor vector process (e.g., the SEL-3378 available for Schweitzer Engineering Laboratories, Inc.) or a real-time automation controller (e.g., the SEL-3530 available from Schweitzer Engineering Laboratories, Inc.). 
       FIG. 3  illustrates another block of an IED  300  for protection and control of an electric power delivery system. As illustrated, IED  300  may include a processor  302 , a random access memory (RAM)  304 , a communications interface  306 , a user interface  308 , and a computer-readable storage medium  310 . The processor  302 , RAM  304 , communications interface  306 , user interface  308 , and computer-readable storage medium may be communicatively coupled to each other via a common data bus  312 . In some embodiments, the various components of IED  300  may be implemented using hardware, software, firmware, and/or any combination thereof. 
     The user interface  308  may be used by a user to enter user defined settings such as, for example, an amount of load to shed for each event level, load priority information, and the like (e.g., the parameters included in the user adjustable parameter module  202  of  FIG. 2 ). The user interface  308  may be integrated in the IED  300  or, alternatively, may be a user interface for a laptop or other similar device communicatively coupled with the IED  300 . Communications interface  306  may be any interface capable of communicating with IEDs and/or other electric power system equipment communicatively coupled to IED  300 . For example, communications interface  306  may be a network interface capable of receiving communications from other IEDs over a protocol such as the IEC 61850 or the like. In some embodiments, communications interface  306  may include a fiber-optic or electrical communications interface for communicating with other IEDs. 
     The processor  302  may include one or more general purpose processors, application specific processors, microcontrollers, digital signal processors, FPGAs, or any other customizable or programmable processing device. The processor  302  may be configured to execute computer-readable instructions stored on the computer-readable storage medium  310 . In some embodiments, the computer-readable instructions may be computer executable functional modules. For example, the computer-readable instructions may include an UF load shedding module  314  configured to cause the processor to perform the UF load shedding operations and a time alignment module  316  used time-aligning and coordinating various communications to and from IEDs connected to the IED, as described in reference to  FIG. 2 . The computer-readable instructions may also include any of the functional modules described in reference to  FIG. 2  to implement the functionality of the IED  200  described therein. 
       FIG. 4  illustrates one embodiment of a method  400  for protection and control of an electric power delivery system. At  402 , a central IED may receive system information from a remote IEDs each associated with a load. In certain embodiments, the system information may include information relating to the operating frequencies of the loads, the power consumption of the loads, synchrophasor information, an indication that an operating frequency of a load has reached a predetermined level, and the like. Based on this system information, at  404 , the central IED may determine which loads are associated with a particular sub-grid of the electric power delivery system experiencing an UF condition. In certain embodiments, determining which loads which loads are associated with a particular sub-grid of the electric power delivery system is based on the decay rates and/or decay times of operating frequencies of the loads. At step  406 , the central IED may determine whether to disconnect one or more loads associated with the sub-grid from the electric power delivery system to mitigate the UF condition, sending a signal to IEDs associated with the one or more loads directing the IEDs to disconnect the loads. As discussed above, in some embodiments, determining which loads to disconnect from the electric power delivery system may be based on priority information associated with the loads. 
     In another embodiment, underfrequency rotor speed conditions (which may include rotor speeds, frequencies, rate-of-change-of-speed, or the like) may be determined using rotor angles. As used herein, the frequency of a generator may be referred to as rotor speed. As described above, a central IED may receive system information from remote IEDs each associated with a load, where the system information may include a frequency and/or detected UF conditions. In this particular embodiment, synchronous machines may be monitored by IEDs, and the rotor angles of the synchronous machines may be determined by the IEDs and communicated with the central IED for sub-grid determination. IEDs may determine rotor position or frequency using, for example, a toothed wheel and a magnetic pickup unit. It should be understood that various systems for determining a rotor position or rotor frequency may be used such as, for example, optical rotor position sensors, mechanical rotor position sensors, toothed wheel sensors, and the like. Rotor position may be used by the IED to determine rotor frequency, rate of change of frequency, rotor angle, power angle, or the like. 
       FIG. 5A  illustrates a conceptual diagram of a rotor  504  of a synchronous generator consistent with embodiments disclosed herein. A rotor  504  may be driven by an external torque (not shown) to induce an electromagnetic field (EMF) in a stationary stator (e.g., stator  553  illustrated in  FIG. 5B ). The rotor  504  includes a field winding  558  wrapped around a rotor body, and the stator includes an armature winding wrapped around an armature body. A direct current is made to flow in the field winding  558  (using, for example, an exciter voltage  560 ) to generate a magnetic field in the rotor  504 . Additionally or alternatively, permanent magnets may also be used. 
       FIG. 5B  illustrates a 3-phase synchronous generator that includes three sets of stator windings  553   a  to  553   a ′,  553   b  to  553   b ′, and  553   c  to  553   c ′ consistent with embodiments disclosed herein. The stator windings are each separated by 120° such that when an electrical field associated with the rotor  504  passes, the electrical currents induced in terminal pairs  555   a  and  555   a ′,  555   b  and  555   b ′, and  555   c  and  555   c ′ are each separated by 120 electrical degrees. When the rotor  504  rotates, as indicated by arrow  510 , the magnetic field rotates with it, passing the stator windings and inducing a time-varying electric current therein. As the poles of the electrical field associated with the rotor  504  pass the stator windings, the voltage present on the corresponding terminals oscillates, and an alternating current results. Thus, the angular position of the rotor  504  is related to the time-varying electrical output of the terminals  555   a - c . As described below, this relationship can be influenced by, for example, an electrical load connected to the terminals of the generator. 
     The period (T I ) of the resulting alternating current from a synchronous generator with N poles, and which has a period of rotation of T G , can be calculated using the formula:
 
 T   I   =NT   G   Eq. 1
 
Embodiments disclosed herein may be applied to any rotor regardless of the number of phases or pairs of poles included therein.
 
     The position of the generator rotor axis is a function of a mechanical power input on the generator and an opposing electrical torque attributed to the electric output from the generator. These opposing forces result in a torque on the rotor. In a steady state condition (i.e., normal operating conditions) these forces are equal in magnitude but opposite in direction. In conditions where the mechanical torque and the electrical torque fall out of balance, the power angle may shift or oscillate, depending on the magnitude and nature of the imbalance. 
       FIG. 6  is one illustration of a power angle curve that shows the relationship between a power angle (δ) and an input mechanical power (P m ). Under balanced conditions, input mechanical power P m  results in equilibrium with the electrical energy drawn from the generator. When the electric torque that balances the mechanical torque decreases (i.e., as a result of an increase in the mechanical power input or a decrease in the electrical load attached to the generator), the rotor rotates at an increased rate, thus causing the power angle to increase. For example, in  FIG. 6 , the mechanical power may increase to P m1  from P m0 , resulting in an increase in the power angle from δ 0  to δ f . In a stable system, the rotor would experience negative acceleration, and eventually come into equilibrium. If the power input exceeds a maximum power input threshold, P max , the generator may become unstable. Knowing the maximum power angle, δ max , and the associated maximum power input threshold, P max , allows an operator to determine how much power can be safely produced by a generator without causing the generator to become unstable. 
       FIG. 7  illustrates a simplified partial cross-sectional view of an MPU  700  consistent with embodiments disclosed herein. MPU  700  is operable to track the passing of a plurality of teeth  712   a - c  associated with a tooth wheel  710  and may be utilized in connection with an electrical generator (not shown). A shaft connected to a rotor (not shown) of the generator may pass through aperture  730  of tooth wheel  710 . MPU  700  includes a magnet  706 , which in certain embodiments may be permanent, a pole-piece  702 , a sensing coil  704 , and a case  708 . Case  708  may extend through a housing  709 . An air gap  726  separates tooth wheel  710  from MPU  700 . Coil  704  may be disposed around a pole-piece  702 , which is disposed across air gap  726  from the plurality of teeth  712   a - c . Pole piece  702  abuts permanent magnet  706 . A connector  707  may be used to connect MPU  700  to an IED (not shown) or other device configured to monitor the power angle of a generator associated with MPU  700 . 
     The passing of the plurality of teeth  712   a - c  in proximity to pole-piece  702  causes a distortion of the magnetic flux field passing through the sensing coil  704  and pole-piece  702 , which in turn generates a signal voltage. In certain embodiments, tooth wheel  710  may be formed of ferrous material. The voltage induced in sensing coil  704  is proportional to the rate of change of flux in the magnetic field, where the rate of change of flux is determined by the size of the air gap  726 , and the rotational velocity of the tooth wheel  710 , as provided in Eq. 2. 
                   ɛ   =       -   N     ⁢       d   ⁢           ⁢   Φ     dt               Eq   .           ⁢   2               
In Eq. 2, ε represents the voltage induced in the sensing coil  704 , N represents the number of coil turns in the sensing coil  704 , and Φ represents the flux in the magnetic field generated by permanent magnet  706 . A plurality of leads  705  may be used to transmit the signal generated by MPU  700  to an IED or other device. The frequency of the induced voltage is proportional to the number of teeth on the wheel and the speed of rotation, according to Eq. 3.
 
                     Frequency   ⁢           ⁢     (   Hz   )       =       Number   ⁢           ⁢   of   ⁢           ⁢   Teeth   *   RPM     60             Eq   .           ⁢   3               
An IED, such as IED  300 , in electrical communication with the MPU or other rotor sensor may receive the electrical signals therefrom to detect a rotor position of the synchronous machine. With the rotor position, the IED may be calculate the frequency of the synchronous machine in accordance with Equation 3. The IED may also be configured to determine a rotor angle and/or power angle of the synchronous machine using the rotor position, frequency, time, and/or available current and/or voltage information from the power system. The IED may be configured to determine a UF event using the frequency calculated using the MPU or other such sensor as described herein. The IED may communicate the UF event along with a time thereof to a central IED such as IED  102  of  FIG. 1 . IED  102  may then use the UF events and time stamps of several IEDs to determine which IEDs are on the same sub-grid. As described in further detail herein, equipment on common isolated sub-grids may experience similar UF events at similar times. Furthermore, equipment on common isolated sub-grids may experience similar frequencies, and similar rates-of-change-of-frequencies at similar times. Thus, a central IED may be configured to use the time-stamped UF events, frequencies, rates-of-change-of-frequencies, or the like from several IEDs to determine which IEDs of the several IEDs are on common isolated sub-grids. Rotor angles (and hence mechanical speed and acceleration) are related to the electrical power system phase angle, frequency, and rate-of-change-of-frequency by the synchronous machine pole counts by the square of the pole count. For example, the rotor speed equals the frequency multiplied by two divided by the pole count.
 
       FIG. 8  illustrates a block diagram of an IED that may be used to collect signals from the generator, determine rotor position, frequency, rate-of-change-of-speed, rotor angle, power angle, and the like from a generator. IED  800  includes a network interface  832  configured to communicate with a data network. IED  800  also includes a time input  840 , which may be used to receive a time signal. In certain embodiments, time input  840  may be used to generate a reference signal, as described above. In certain embodiments, a common time reference may be received via network interface  832 , and accordingly, a separate time input and/or GPS input  836  would not be necessary. One such embodiment may employ the IEEE 1588 protocol. Alternatively, a GPS input  836  may be provided in addition or instead of a time input  840 . 
     A monitored equipment interface  829  may be configured to receive status information from, and issue control instructions to a piece of monitored equipment, such as an electrical generator. According to certain embodiments, the monitored equipment interface  829  may be configured to interface with an MPU and/or Hall-Effect sensor that generates a signal based upon the detection of the passage of one or more teeth associated with a tooth wheel coupled to a rotor in an electrical generator. 
     A computer-readable storage medium  826  may be the repository of one or more modules and/or executable instructions configured to implement any of the processes described herein. A data bus  842  may link monitored equipment interface  829 , time input  840 , network interface  832 , GPS input  836 , and computer-readable storage medium  826  to a processor  824 . 
     Processor  824  may be configured to process communications received via network interface  832 , time input  840 , GPS input  836 , and monitored equipment interface  829 . Processor  824  may operate using any number of processing rates and architectures. Processor  824  may be configured to perform various algorithms and calculations described herein using computer executable instructions stored on computer-readable storage medium  826 . Processor  824  may be embodied as a general purpose integrated circuit, an application specific integrated circuit, a field-programmable gate array, and other programmable logic devices. 
     In certain embodiments, IED  800  may include a sensor component  850 . In the illustrated embodiment, sensor component  850  is configured to gather data directly from a conductor (not shown) using a current transformer  802  and/or a voltage transformer  814 . Voltage transformer  814  may be configured to step-down the power system&#39;s voltage (V) to a secondary voltage waveform  812  having a magnitude that can be readily monitored and measured by IED  800 . Similarly, current transformer  802  may be configured to proportionally step-down the power system&#39;s line current (I) to a secondary current waveform  804  having a magnitude that can be readily monitored and measured by IED  800 . Low pass filters  808 ,  816  respectively filter the secondary current waveform  804  and the secondary voltage waveform  812 . An analog-to-digital converter  818  may multiplex, sample and/or digitize the filtered waveforms to form corresponding digitized current and voltage signals. 
     As described above, certain embodiments may monitor the terminal voltage of one or more phases of electrical power generated by an electrical generator. Sensor component  850  may be configured to perform this task. Further, sensor component  850  may be configured to monitor a wide range of characteristics associated with monitored equipment, including equipment status, temperature, frequency, pressure, density, infrared absorption, radio-frequency information, partial pressures, viscosity, speed, rotational velocity, mass, switch status, valve status, circuit breaker status, tap status, meter readings, and the like. 
     A/D converter  818  may be connected to processor  824  by way of a bus  842 , through which digitized representations of current and voltage signals may be transmitted to processor  824 . In various embodiments, the digitized current and voltage signals may be compared against conditions. For example, certain conditions may be established in order to implement one or more control actions based upon a determination that a power angle exceeds a threshold. The control action may include an instruction to reduce the load connected to the generator (e.g., by load shedding) or an instruction to increase generation capacity. 
     A monitored equipment interface  829  may be configured to receive status information from, and issue control instructions to a piece of monitored equipment. As discussed above, control actions may be issued when the power angle of a generator is outside of an acceptable range in order to cause the power angle to return to the acceptable range. Monitored equipment interface  829  may be configured to issue control instructions to one or more pieces of monitored equipment. According to some embodiments, control instructions may also be issued via network interface  832 . Control instructions issued via network interface  832  may be transmitted, for example, to other IEDs (not shown), which in turn may issue the control instruction to a piece of monitored equipment. Alternatively, the piece of monitored equipment may receive the control instruction directly via its own network interface. 
     Computer-readable storage medium  826  may be the repository of one or more modules and/or executable instructions configured to implement certain functions described herein. For example, a signal module  852  may be configured to generate or analyze a reference signal and/or a rotational position signal. Signal module  852  may further be configured to detect a relative shift between the reference signal and the rotational position signal. The rotational position module  853  may be configured to determine the rotational position of the rotor based upon the relative shift between the reference signal and the rotational position signal. Further, the rotational position module  853  may be configured to determine whether the rotational position is within an acceptable range. The determination of whether the rotational position is within an acceptable range may be used to determine when control actions are to be implemented in order to cause the rotational position to return to the acceptable range. Control instruction module  854  may be configured to issue appropriate control instructions in order to maintain the electrical generator within the acceptable range or to cause the rotational position to return to the acceptable range. Communication module  855  may facilitate communication between IED  800  and other IEDs (not shown) via network interface  832 , such as the central IED. In addition, communication module  755  may further facilitate communication with monitored equipment in communication with IED  800  via monitored equipment interface  829  or with monitored equipment in communication with IED  800  via network interface  832 . 
       FIG. 9  illustrates another simplified diagram of an electric power generation and delivery system similar to that of  FIG. 1 . The system illustrated in  FIG. 9  includes IEDs  952 ,  954 ,  956 , and  958 , each in communication with and configured to monitor and protect generators  110 ,  112 ,  114 , and  116 , respectively. IEDs  952 - 958  may be configured to monitor a rotational position of the rotors of their connected generators, determine rotor position, frequency, rate-of-change-of-speed, rotor angle, and/or power angle as described herein. IEDs  952 - 958  may further be configured to transmit the determined rotor position, frequency, rate-of-change-of-speed, rotor angle, and/or power angle to the central IED  102 . Central IED  102  may be configured to determine which generators are connected to common isolated sub-grids according to the various embodiments described herein. 
     For example, when IED  952  determines that generator  110  is experiencing an underfrequency condition using rotor position information therefrom, and IED  954  determines that generator  112  is experiencing an underfrequency condition using rotor position information therefrom within a predetermined time of the detection from IED  952 , central IED  102  may determine that generators  110  and  112  are on a common isolated sub-grid. The predetermined time may be, for example, 2 seconds. In another embodiment, the predetermined time may be 0.5 seconds. Furthermore, if the remaining IEDs did not communicate such underfrequency condition, then the central IED may determine that generators  110  and  112  are on a common isolated sub-grid that is separate from the other generators of the system. 
     While specific embodiments and applications of the disclosure have been illustrated and described, it is to be understood that the disclosure is not limited to the price configurations and components disclosed herein. For example, the systems and methods described herein may be applied to an industrial electric power delivery system or an electric power delivery system implemented in a boat or oil platform that may not include long-distance transmission of high-voltage power. Moreover, principles described herein may also be utilized for protecting an electrical system from over-frequency conditions, wherein power generation would be shed rather than load to reduce effects on the system. Accordingly, many changes may be made to the details of the above-described embodiments without departing from the underlying principles of this disclosure. The scope of the present invention should, therefore, be determined only by the following claims.