Patent Publication Number: US-11650241-B1

Title: Incremental quantities-based fault locating technique and system

Description:
BACKGROUND 
     This disclosure relates to locating faults in electric power delivery systems. More particularly, this disclosure relates to determining a fault location in electric power delivery systems by using incremental quantities. 
     This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present techniques, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of any kind. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a block diagram of a system for determining a fault location using the incremental quantities, in accordance with an embodiment; 
         FIG.  2    illustrates an equivalent three-phase network with a local Terminal L and a remote Terminal R, with a fault on a line between terminals L and R, in accordance with an embodiment; and 
         FIG.  3    is a flowchart of a method for determining a location of a fault using the incremental quantities, in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     One or more specific embodiments will be described below. In an effort to provide a concise description of these embodiments, not all features of an actual implementation are described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. Certain examples commensurate in scope with the originally claimed subject matter are discussed below. These examples are not intended to limit the scope of the disclosure. Indeed, the present disclosure may encompass a variety of forms that may be similar to or different from the examples set forth below. 
     When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Additionally, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. Furthermore, the phrase A “based on” B is intended to mean that A is at least partially based on B. Moreover, unless expressly stated otherwise, the term “or” is intended to be inclusive (e.g., logical OR) and not exclusive (e.g., logical XOR). In other words, the phrase “A or B” is intended to mean A, B, or both A and B. 
     As used herein, the terms “connect,” “connection,” “connected,” “in connection with,” and “connecting” are used to mean “in direct connection with” or “in connection with via one or more elements”; and the term “set” is used to mean “one element” or “more than one element.” Further, the terms “couple,” “coupling,” “coupled,” “coupled together,” and “coupled with” are used to mean “directly coupled together” or “coupled together via one or more elements.” 
     In addition, as used herein, the terms “real time”, “real-time”, or “substantially real time” may be used interchangeably and are intended to describe operations (e.g., computing operations) that are performed without any human-perceivable interruption between operations. For example, as used herein, data relating to the systems described herein may be collected, transmitted, and/or used in control computations in “substantially real time” such that data readings, data transfers, and/or data processing steps occur once every second, once every 0.1 second, once every 0.01 second, or even more frequent, during operations of the systems (e.g., while the systems are operating). In addition, as used herein, the terms “continuous”, “continuously”, or “continually” are intended to describe operations that are performed without any significant interruption. For example, as used herein, control commands may be transmitted to certain equipment every five minutes, every minute, every 30 seconds, every 15 seconds, every 10 seconds, every 5 seconds, or even more often, such that operating parameters of the equipment may be adjusted without any significant interruption to the closed-loop control of the equipment. In addition, as used herein, the terms “automatic”, “automated”, “autonomous”, and so forth, are intended to describe operations that are performed are caused to be performed, for example, by a computing system (i.e., solely by the computing system, without human intervention). Indeed, although certain operations described herein may not be explicitly described as being performed continuously and/or automatically in substantially real time during operation of the computing system and/or equipment controlled by the computing system, it will be appreciated that these operations may, in fact, be performed continuously and/or automatically in substantially real time during operation of the computing system and/or equipment controlled by the computing system to improve the functionality of the computing system (e.g., by not requiring human intervention, thereby facilitating faster operational decision-making, as well as improving the accuracy of the operational decision-making by, for example, eliminating the potential for human error), as described in greater detail herein. 
     The embodiments of the disclosure will be best understood by reference to the drawings, wherein like parts are designated by like numerals throughout. 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 need the steps 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. The components of the embodiments as generally described and illustrated in the figures could be arranged and designed in a wide variety of different configurations. 
     Several aspects of the embodiments described may be implemented 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 and/or transmitted as electronic signals over a system bus or wired or wireless network. A software module or component may, for instance, include physical or logical blocks of computer instructions, which may be organized as a routine, program, object, component, data structure, or the like, and which performs a task or implements a particular abstract data type. 
     In certain embodiments, a particular software module or component may include 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 include 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 tangible, non-transitory, computer-readable and/or machine-readable medium having stored thereon instructions that may be used to program a computer (or other electronic device) to perform processes described herein. For example, a non-transitory computer-readable medium may store instructions that, when executed by a processor of a computer system, cause the processor to perform certain methods disclosed herein. The non-transitory computer-readable medium may include, but is not limited to, hard drives, floppy diskettes, optical disks, compact disc read-only memories (CD-ROMs), digital versatile disc read-only memories (DVD-ROMs), read-only memories (ROMs), random access memories (RAMs), erasable programmable read-only memories (EPROMs), electrically erasable programmable read-only memories (EEPROMs), magnetic or optical cards, solid-state memory devices, or other types of machine-readable media suitable for storing electronic and/or processor executable instructions. 
     With the forgoing in mind, the present disclosure is related to electric power delivery systems and improved systems and method for identifying fault locations in power delivery systems. Before continuing, it should be understood that faster transmission line protection improves power system stability in power delivery systems. If faults are not cleared before the critical fault clearing time, the system may lose transient stability and possibly suffer a black out. In addition, faster fault clearing increases the amount of power that can be transferred. Faster protection also enhances public and utility personnel safety, limits equipment wear, improves power quality, and reduces property damage. 
     Most protection principles are based on the fundamental frequency components of voltages and currents. Accurate measurement of a sinusoidal quantity typically takes a cycle. An analysis of transient components may be undertaken in connection with various embodiments of the present disclosure. Further, information relating to electrical conditions may be communicated among devices to provide end-to-end transmission line protection. 
     Various embodiments consistent with the present disclosure may analyze incremental quantities, which are determined by real-time signals that appear due to a fault and do not contain load voltages or currents. Incremental quantities may simplify the line and system representation by eliminating power sources and leaving the fault as the only “source” in the equivalent network. By way of example, instantaneous electrical measurements associated with a loop in a multiple-phase electric power delivery system may be obtained before a fault occurred on the loop and after the same fault occurred on the same loop, and differences between the instantaneous electrical measurements at different time may give insight into information related to the fault (e.g., fault location). 
     In certain embodiments, sensors (e.g., electrical sensors, temperature sensors, intelligent electronic devices (IEDs), and so forth) may be used and powered by a battery (e.g., rechargeable battery, either standing alone or connected to a power system, which may be charged when power is available), or by an additional power supply (e.g., power backup system, solar panel power system or other alternative power system, and so forth), or any combination of them (e.g., converting to other power supply methods when there is an outage on one power supply). The sensors may be coupled to an existing monitoring system, or stand alone. The sensors may be installed on a mobile device. The sensors may be used to monitor the electric power delivery system for a period of time. As such, the sensors may work on a demand, may be easily coupled to an existing system, may be portable. In certain embodiments, the sensors may measure values of electrical operating parameters of a particular loop in a multiple-phase electric power delivery system, and send the sensor data to an electrical monitoring system. 
     In certain embodiments, the electrical monitoring system may receive instantaneous measurements of electrical operating parameters at a local terminal and a remote terminal on a particular loop before a fault occurred on the loop, such that the fault occurred at a location between the local terminal and the remote terminal. The electrical monitoring system may then receive instantaneous measurements of electrical operating parameters at the local terminal and the remote terminal of the particular loop after the fault occurred on the loop. With this in mind, the electrical monitoring system may compare the values of the operating parameters measured at the local terminal (or the remote terminal) before the fault occurred on the loop and after the fault occurred on the same loop to obtain respective incremental quantities for the local terminal (or the remote terminal). 
     In certain embodiments, the electrical monitoring system may then use incremental quantities for a local terminal and a remote terminal on a particular loop to determine the fault location between the local terminal and the remote terminal by using methods and techniques described in greater detail herein. The electrical monitoring system may send instructions to activate certain actions (e.g., protective actions) based on the determined fault location. 
     In certain embodiments, the electrical monitoring system may monitor incremental quantities for local terminals and remote terminals on more than one loops in a multiple-phase electric power delivery system in order to determine the fault location on a particular loop. For instance, a ground fault situation and location may be identified by the electrical monitoring system based on the monitored incremental quantities for respective local terminals and respective remote terminals on multiple loops within the multiple-phase electric power delivery system. Indeed, by monitoring the incremental quantities for respective local terminal and respective remote terminal on the multiple loops, the electrical monitoring system may be able to determine the fault locations on additional loops of the multiple-phase electric power delivery system. In addition, each of the above described embodiments may be performed continuously to provide for real-time monitoring and fault location identification. 
     By way of introduction,  FIG.  1    illustrates a block diagram of a system  100  for determining and calculating a location of a fault using incremental quantities further described herein. System  100  may include generation, transmission, distribution and/or similar systems. System  100  includes a conductor  106 , such as a transmission line connecting two nodes, which are illustrated as a local terminal  112  and a remote terminal  114 . The local terminal  112  and the remote terminal  114  may be part of buses in a transmission system supplied by generators  116  and  118 , respectively. Although illustrated in single line form for purposes of simplicity, system  100  may be a multi-phase system, such as a three-phase electric power delivery system. 
     System  100  may be monitored by IEDs (or other suitable sensors, such as electrical sensors or temperature sensors, and so forth)  102  and  104  at two locations of the system, although further IEDs may also be utilized to monitor further locations of the system. As used herein, an IED (such as IEDs  102  and  104 ) may refer to any microprocessor-based device that monitors, controls, automates, and/or protects monitored equipment within system  100 . Such devices 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, and the like. The term IED may be used to describe an individual IED or a system comprising multiple IEDs. The IEDs  102  and  104  may obtain electric power system information using current transformers (CTs), potential transformers (PTs), Rogowski coils, voltage dividers and/or the like. The IEDs  102 ,  104  may be capable of using inputs from conventional instrument transformers such as CTs and PTs conventionally used in monitoring of electric power delivery. The IEDs  102  and  104  may also receive common time information from a common time source  110 . 
     A common time source  110  may be any time source capable of delivering a common time signal to each of IEDs  102  and  104 . Some examples of a common time source include a Global Navigational Satellite System (GNSS) such as the Global Positioning System (GPS) delivering a time signal corresponding with IRIG, a WVWB or WVW system, a network-based system such as corresponding with IEEE 1588 precision time protocol, and/or the like. According to one embodiment, common time source  110  may comprise a satellite-synchronized clock (e.g., Model No. SEL-2407, available from SEL). Further, it should be noted that each IED  102 ,  104  may be in communication with a separate clock, such as a satellite-synchronized clock, with each clock providing each IED  102 ,  104  with a common time signal. The common time signal may be derived from a GNSS system or other time signal. 
     A data communication channel  108  may allow the IEDs  102  and  104  to exchange information relating to, among other things, voltages, currents, fault detections, fault locations, and the like. According to some embodiments, a time signal based on common time source  110  may be distributed to and/or between IEDs  102  and  104  using data communication channel  108 . Data communication channel  108  may be embodied in a variety of media and may utilize a variety of communication protocols. For example, the data communication channel  108  may be embodied utilizing physical media, such as coaxial cable, twisted pair, fiber optic, etc. Further, the data communication channel  108  may utilize communication protocols such as Ethernet, SONET, SDH, or the like, in order to communicate data. 
     In several embodiments herein, incremental quantities may be used to determine and calculate location of a fault. Fault related voltages and current signals are determined directly from time synchronized signals. These fault signals are a sum of pre-fault signals and fault-generated signals. Hence, the fault generated signals are a difference between fault signals and the pre-fault signals. One simple method to compute incremental quantities is:
 
Δ s   (t)   =s   (t)   −s   (t-PT)   (1)
 
where Δs (t)  is the instantaneous incremental quantity at time t, s (t)  is the measured instantaneous value of a quantity at time t, T is the period of the measured quantity, p is an arbitrary number of periods, and s (t-pT)  is the measured instantaneous value of the quantity at time (t-pT). That is, the instantaneous incremental quantity at time t is determined by comparing the measured instantaneous values of the quantity at time t and at time (t-pT). Using the above equation, an instantaneous incremental quantity that lasts for p power cycles can be obtained. The value of p may be selected based on the intended usage of the instantaneous incremental quantity. For example, if the incremental quantities are intended to be used during two power cycles, p can be more than 2.
 
     With this in mind, the incremental quantities may be used to determine a location of a fault within an electrical network. For instance,  FIG.  2    illustrates an equivalent three-phase network that has a fault on phase AG (i.e., phase A to ground) between terminals L  112  and R  114  consistent with certain embodiments of the present disclosure. The terminal L  112  and the remote Terminal R  114  may include sensor units that detect electrical properties, such as voltage and current, at the respective locations in the three-phase network. The fault network contains incremental voltages and currents that may be used for protection of the network as further described herein. Based on the fault network illustrated in  FIG.  2   , fault voltage Δv F  may be determined based on measurements acquired at the terminal L  112 . That is, at the terminal L  112  of the network, the instantaneous incremental voltage between phase A and ground Δv AL , and the instantaneous incremental currents Δi AL , Δi BL , Δi CL  are related by a simple voltage drop equation across the terminal L  112  illustrated by equation (in the phasor domain):
 
Δ V   AL   −m ·( Z   s   ΔI   AL   +Z   m ·(Δ I   BL   +ΔI   CL ))=Δ V   F   (2)
 
where Z s  is self-impedance of transmission line impedance, Z m  is the mutual impedance between the phases, and m is the per unit fault location from the terminal L  112 . In some embodiments, it may be assumed that the system has balanced impedances, which means symmetrical lines, and Z s  and Z m  are both complex quantities. As such, equation (2) above can be written as:
 
Δ V   AL   −m ·( Z   s   ΔI   AL   −Z   m   ·ΔI   AL   +Z   m ·(Δ I   AL   +ΔI   BL   +ΔI   CL ))=Δ V   F   (3)
 
Where ΔV AL  represents the phasor fault voltage between phase A and ground at the fault location. Now, setting 3ΔI 0L  equal to ΔI AL +ΔI BL +ΔI CL  as provided in equation (4) below, equation (3) can be rewritten as equations (5A and 5B)
 
                       Δ   ⁢     I   AL       +     Δ   ⁢     I   BL       +     Δ   ⁢     I   CL         =     3   ⁢   Δ   ⁢     I     0   ⁢   L                 (   4   )                               Δ   ⁢     V   AL       -     m   ·     (           (       Z   s     -     Z   m       )     ·   Δ     ⁢     I   AL       +       Z   m     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   L         )         )         =     Δ   ⁢     V   F               (     5   ⁢   A     )                               Δ   ⁢     V   AL       -     m   ·     (           Z     1   ⁢   T       ·   Δ     ⁢     I   AL       +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   L         )         )         =     Δ   ⁢     V   F               (     5   ⁢   B     )               
Here, for a transmission line system with balanced impedances,
 
                     Z     1   ⁢   T       =       Z   s     -     Z   m               (   6   )                             Z   m     =       (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3             (   7   )               
Z 1T  and Z 0T  are the positive sequence and the zero-sequence transmission line impedances, respectively, for a system with balanced impedances.
 
Similarly, the incremental voltage from the remote side (with subscript “R” indicating terminal R) is expressed in Equation 5C:
 
                       Δ   ⁢     V     A   ⁢   R         -       (     1   -   m     )     ·     (           Z     1   ⁢   T       ·   Δ     ⁢     I     A   ⁢   R         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   R         )         )         =     Δ   ⁢     V   F               (     5   ⁢   C     )               
By applying equations (6) and (7) to equations (5), and equating equations 5B and 5C, equations (8) may be expressed as follows:
 
                       Δ   ⁢     V     A   ⁢   L         -     m   ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     A   ⁢   L         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   L         )         )         =       Δ   ⁢     V     A   ⁢   R         -       (     1   -   m     )     ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     A   ⁢   R         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   R         )         )                 (     8   ⁢   A     )                               Δ   ⁢     V     A   ⁢   L         -     Δ   ⁢     V     A   ⁢   R           =       m   ·       Z     1   ⁢   T       (       Δ   ⁢     V     A   ⁢   L         +     Δ   ⁢     V     A   ⁢   R           )       +     m   ·     (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     ·     (       Δ   ⁢     I     0   ⁢   L         +     Δ   ⁢     I     0   ⁢   R           )       -         Z     1   ⁢   T       ·   Δ     ⁢     I     A   ⁢   R         -       (       Z     0   ⁢   T       -         Z     1   ⁢   T         )     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   R         )                 (     8   ⁢   B     )               
Where:
 
                 Δ   ⁢     I   Z       =         Z     1   ⁢   T       ·     (     Δ   ⁢   I     )           ❘   &#34;\[LeftBracketingBar]&#34;       Z     1   ⁢   T         ❘   &#34;\[RightBracketingBar]&#34;           ;         
and,
 
               Δ   ⁢     I     Z   ⁢   0         =     -         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     ·     (     Δ   ⁢     I   0       )           ❘   &#34;\[LeftBracketingBar]&#34;       Z     1   ⁢   T         ❘   &#34;\[RightBracketingBar]&#34;                 
Now we have equation 9 in phasor-domain quantities:
 
Δ V   AL   −ΔV   AR   =m·|Z   1T |(Δ I   Z,AL   −ΔI   Z,0L   +ΔI   Z,AR   −ΔI   Z,0R )−| Z   1T |·(Δ I   Z,AR   −ΔI   Z,0R )  (9)
 
     Using phasor-domain quantities may introduce delays as long as one cycle. In systems with inverter-based resources, for example, the fault data may not be available for even as long as one cycle. Inverters act fast and usable data available could be less than one cycle. Accordingly, the presently disclosure introduces methods using instantaneous incremental quantities to capture necessary data without significant delay. 
     Accordingly, equation 9 may be analyzed in time-domain as described below. Equation 10 may be used to obtain instantaneous replica currents, 
                     Δ   ⁢     i   Z       =     (           R     1   ⁢   T           ❘   &#34;\[LeftBracketingBar]&#34;       Z     1   ⁢   T         ❘   &#34;\[RightBracketingBar]&#34;         ·     (     Δ   ⁢   i     )       +         L     1   ⁢   T           ❘   &#34;\[LeftBracketingBar]&#34;       Z     1   ⁢   T         ❘   &#34;\[RightBracketingBar]&#34;         ·       d   ⁡   (     Δ   ⁢   i     )       d   ⁢   t           )             (   10   )               
Where:
 
     
       
         
           
             
               
                 
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     Using instantaneous replica currents, Equation 9 may be written in instantaneous form as Equation 11:
 
Δ v   AL   −Δv   AR   =m·|Z   1T |(Δ i   Z,AL   −Δi   Z,0L   +Δi   Z,AR   −Δi   Z,0R )−| Z   1T |·(Δ i   Z,AR   −Δi   Z,0R )  (11)
 
Then, m, the per unit fault location from terminal L  112 , is determined by
 
     
       
         
           
             
               
                 
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     For the same AG fault, the BG loop may also be considered as shown below: 
                       Δ   ⁢     V     B   ⁢   L         -     m   ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     B   ⁢   L         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   L         )         )       +       (     1   -   m     )     ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     B   ⁢   R         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   R         )         )       -     ΔV     B   ⁢   R         =   0           (   13   )               
Here, ΔI BL ˜0, ΔI BR ˜0, because the fault is an AG fault and there should be no or a negligible amount of change in the B-phase current at both local and remote terminals.
 
Equation 13 may be solved for the BG loop similar to the solution of the AG loop, above in the time domain becomes equation 14:
 
Δ v   BL   −Δv   BR   =m·|Z   1T |(Δ i   Z,BL   −Δi   Z,0L   +Δi   Z,BR   −Δi   Z,0R )−| Z   1T |·(Δ i   Z,BR   −Δi   Z,0R )  (14)
 
And the per unit fault location from terminal L  112 , is determined by
 
     
       
         
           
             
               
                 
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                   15 
                   ) 
                 
               
             
           
         
       
     
     For the same AG fault, now consider the AB loop: 
                       Δ   ⁢     V     A   ⁢   L         -     m   ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     A   ⁢   L         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   L         )         )       +       (     1   -   m     )     ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     A   ⁢   R         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·         (     3   ⁢   Δ   ⁢     I     0   ⁢   R         )         )       -         Δ   ⁢     V     A   ⁢   R         +     Δ   ⁢     V     B   ⁢   R         -       (     1   -   m     )     ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     B   ⁢   R         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·     (     3   ⁢   Δ   ⁢     I     0   ⁢   R         )         )       +         m   ·     (         Z     1   ⁢   T       ⁢   Δ   ⁢     I     B   ⁢   L         +         (       Z     0   ⁢   T       -     Z     1   ⁢   T         )     3     ·         (     3   ⁢   Δ   ⁢     I     0   ⁢   L         )         )       -     Δ   ⁢     V     B   ⁢   L           =   0           (   16   )               
Solving Equation 16 following the solution to the AG loop in the time domain yields equation 17:
 
Δ v   AL   −m·|Z   1T |·(Δ i   Z,AL   −Δi   Z,0L )+(1− m )·| Z   1T |·(Δ i   Z,AR   −Δi   Z,0R )−Δ v   AR   +Δv   BR −(1− m )·| Z   1T |·(Δ i   Z,BR   −Δi   Z,0R )+ m·|Z   1T |·(Δ i   Z,BL   −Δi   Z,0L )−Δ v   BL =0  (17)
 
The per unit fault location from terminal L  112 , is determined by
 
     
       
         
           
             
               
                 
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                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     It can be shown that m obtained from the AB loop, i.e. Equation (18), is the same as the m obtained from the AG loop, i.e. Equation (12). Equation (18) can be rearranged as:
 
Δ v   AL   −Δv   AR   −m·|Z   1T |(Δ i   Z,AL   +Δi   Z,AR )+| Z   1T |·(Δ i   Z,AR )=Δ v   BL   −Δv   BR   −m·|Z   1T |(Δ i   Z,BL   +Δi   Z,BR )+| Z   1T |·(Δ i   Z,BR )  (19)
 
Substituting equation (15),
 
Δ v   AL   −ΔV   AR   −m·|Z   1T |(Δ i   Z,AL   +Δi   Z,AR )+| Z   1T |·(Δ i   Z,AR )= m·|Z   1T |(Δ i   Z,BL   −Δi   Z,0L   +Δi   Z,BR   −Δi   Z,0R )−| Z   1T |·(Δ i   Z,BR   −Δi   Z,0R )− m·|Z   1T |(Δ i   Z,BL   +Δi   Z,BR )+| Z   1T |·(Δ i   Z,BR )  (20)
 
Here, Δi Z,BL ˜0; Δi Z,BR ˜0, because the fault is an AG fault and there should be no or a negligible amount of change in the B-phase current at both local and remote terminals.
 
Δ v   AL   −Δv   AR   −m·|Z   1T |(Δ i   Z,AL   +Δi   Z,AR )+| Z   1T |·(Δ i   Z,AR )= m·|Z   1T |(−Δ i   Z,0L   −Δi   Z,0R )−| Z   1T |·(−Δ i   Z,0R )  (21)
 
Therefore,
 
     
       
         
           
             
               
                 
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                   22 
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     For the same AG fault, now consider the CG loop in time domain:
 
Δ v   CL   −Δv   CR   =m·|Z   1T |(Δ i   Z,CL   −Δi   Z,0L   +Δi   Z,CR   −Δi   Z,0R )−| Z   1T |·(Δ i   Z,CR   −Δi   Z,0R )  (23)
 
Solving this loop (similar to solving AG loop),
 
     
       
         
           
             
               
                 
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                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     Then, the CA loop result in equation (25), 
                   m   =         (       Δ   ⁢     v     A   ⁢   L         -     Δ   ⁢     v     C   ⁢   L           )     -     (       Δ   ⁢     v     A   ⁢   R         -     Δ   ⁢     v   CR         )     +         ❘   &#34;\[LeftBracketingBar]&#34;       Z     1   ⁢   T         ❘   &#34;\[RightBracketingBar]&#34;       ·     (       Δ   ⁢     i     Z   ,   AR         -     Δ   ⁢     i     Z   ,   CR           )               ❘   &#34;\[LeftBracketingBar]&#34;       Z     1   ⁢   T         ❘   &#34;\[RightBracketingBar]&#34;       ·     {       (       Δ   ⁢     i     Z   ,   AL         -     Δ   ⁢     i     Z   ,   CL           )     +     (       Δ   ⁢     i     Z   ,   AR         -     Δ   ⁢     i     Z   ,   CR           )       }                 (   25   )               
Similar to the AB loop, it can be shown that m obtained from the CA loop is the same as the AG loop.
 
     The BC loop does not give the same per unit fault location m because the fault is an AG fault and there will be no or a negligible amount of change in the B-phase and C-phase currents at both local and remote terminals causing large errors in the per unit fault location computation. In this way, the present embodiments described herein allows for a valid fault location to be obtained as long as the phase involved in the fault is included in the phase-phase loop used for incremental quantities-based fault location calculation. This relationship is illustrated in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Loops and Fault Types 
               
            
           
           
               
               
               
            
               
                   
                 Loop 
                 Detectable Fault Types 
               
               
                   
                   
               
               
                   
                 AG 
                 AG, BG, CG, AB, CA, ABG, BCG, CAG, ABC 
               
               
                   
                 BG 
                 AG, BG, CG, AB, BC, ABG, BCG, CAG, ABC 
               
               
                   
                 CG 
                 AG, BG, CG, BC, CA, ABG, BCG, CAG, ABC 
               
               
                   
                 AB 
                 AG, BG, AB, BC, CA, ABG, BCG, CAG, ABC 
               
               
                   
                 BC 
                 BG, CG, AB, BC, CA, ABG, BCG, CAG, ABC 
               
               
                   
                 CA 
                 AG, CG, AB, BC, CA, ABG, BCG, CAG, ABC 
               
               
                   
                   
               
            
           
         
       
     
     Incremental quantities used for calculation of loops listed in Table 1 are listed in Table 2: 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Incremental quantities for calculation of m 
               
            
           
           
               
               
               
            
               
                 Loop 
                 Voltage 
                 Current 
               
               
                   
               
               
                 AG 
                 Δv AL , Δv AR   
                 (Δi Z, AL  − Δi Z, 0L ), (Δi Z, AR  − Δi Z, 0R ) 
               
               
                 BG 
                 Δv BL , Δv BR   
                 (Δi Z, BL  − Δi Z, 0L ), (Δi Z, BR  − Δi Z, 0R ) 
               
               
                 CG 
                 Δv CL , Δv CR   
                 (Δi Z, CL  − Δi Z, 0L ), (Δi Z, CR  − Δi Z, 0R ) 
               
               
                 AB 
                 (Δv AL  − Δv BL ),  
                 (Δi Z, AL  − Δi Z, BL ), (Δi Z, AR  − Δi Z, BR ) 
               
               
                   
                 (Δv AR  − Δv BR ) 
                   
               
               
                 BC 
                 (Δv BL  − Δv CL ),  
                 (Δi Z, BL  − Δi Z, CL ), (Δi Z, BR  − Δi Z, CR ) 
               
               
                   
                 (Δv BR  − Δv CR ) 
                   
               
               
                 CA 
                 (Δv CL  − Δv AL ),  
                 (Δi Z, CL  − Δi Z, AL ), (Δi Z, CR  − Δi Z, AR ) 
               
               
                   
                 (Δv CR  − Δv AR ) 
               
               
                   
               
            
           
         
       
     
     Because zero-sequence impedance is generally not accurately known, the incremental quantities for three phase-phase loops, i.e. AB, BC, and CA, may be used either in combination or all, to determine fault location for all fault types. 
       FIG.  3    illustrate a flow chart of a method  150  for determining the fault location in accordance with embodiments described herein. Although the following description of the method  150  is described as being performed in a particular order, it should be noted that the method  150  may be performed in any suitable order. Moreover, it should be noted that the method  150  may be performed by any suitable computing system that may have certain processing capabilities. Further, the flow chart in  FIG.  3    may be refined/enhanced based on system requirements. 
     For instance, the computing system may include a communication component, a processor, a memory, a storage, input/output (I/O) ports, a display, and the like. The communication component may facilitate communication between the computing system and the terminals L  112  and R  114  and any other suitable communication-enabled devices. 
     The processor may be any type of computer processor or microprocessor capable of executing computer-executable code. The processor may also include multiple processors that may perform the operations described below. The memory and the storage may be any suitable articles of manufacture that can serve as media to store processor-executable code, data, or the like. These articles of manufacture may represent computer-readable media (e.g., any suitable form of memory or storage) that may store the processor-executable code used by the processor to perform the presently disclosed techniques. The memory and the storage may store data, various other software applications for analyzing the data, and the like. The memory and the storage may represent non-transitory computer-readable media (e.g., any suitable form of memory or storage) that may store the processor-executable code used by the processor to perform various techniques described herein. It should be noted that non-transitory merely indicates that the media is tangible and not a signal. 
     The I/O ports may be interfaces that may couple to other peripheral components such as input devices (e.g., keyboard, mouse), sensors, input/output (I/O) modules, and the like. The display may operate to depict visualizations associated with software or executable code being processed by the processor. In an embodiment, the display may be a touch display capable of receiving inputs from a user. The display may be any suitable type of display, such as a liquid crystal display (LCD), plasma display, or an organic light emitting diode (OLED) display, for example. 
     Referring now to  FIG.  3   , at block  152  and block  154 , the computing system may receive the real-time and synchronized signals of electrical measurements at a first time t1 for a loop from the terminal L  112  and the terminal R  114 . In some embodiments, the terminals L  112  and R  114  may include the IEDs  102  and  104 , respectively, which may measure the electrical properties at the respective locations. The electrical measurements may include voltage measurements, current measurements, and the like in accordance to the equations described above (e.g., equation 2). The IEDs  102  and  104  may then send data related to the electrical measurements to the computing system. 
     At block  156  and block  158 , the computing system may receive the real-time and synchronized signals of electrical measurements at as second time t2 after the first time t1 for a loop from the IEDs  102  and  104  located at the terminal L  112  and the terminal R  114 . At block  160 , the computing system may determine the incremental quantities for the loop according to Table 2. 
     At block  162 , the computing system may determine whether a fault is present based on receiving a notification of a fault trigger from any suitable device. For example, the fault trigger may be received from a remote device, which is outside of the system  100 . The computing system may calculate the incremental quantities in response to receiving the fault trigger. 
     For example, the IED  102  may measure the real-time phase A to ground voltage at the terminal L  112 , v AL (t), at times t1 and t2, and the computing system may calculate the corresponding instantaneous incremental quantity Δv AL  according to:
 
Δ v   AL   =v   AL ( t 2)− v   AL ( t 1).  (27)
 
Similarly, the IED  104  may measure the real-time phase A to ground voltage at position R  114 , v AR (t), at times t1 and t2, and the computing system may calculate the corresponding instantaneous incremental quantity Δv AR  according to:
 
Δ v   AR   =v   AR ( t 2)− v   AR ( t 1).  (28)
 
Here, v AR (t) and v AL (t) are synchronized by the common time source  110 . Similarly, the incremental quantities for currents at the terminal L  112  and the terminal R  114  can be calculated by the computing system.
 
     The above analysis indicates that a valid fault location can be obtained when the phase involved in the fault is included in the phase-phase loop using an incremental quantities-based fault location computation. Also, phase-ground loops give fault locations for most fault types, excluding phase-phase faults that do not involve the phase that is used in the phase-ground loop, but they need to use zero sequence impedance information. Hence, the computing system may use the phase-phase loops to determine fault locations for 9 out of 10 fault types. If all three phase-phase loops are used for fault location computation, the computing system may use 2 out of 3 phase-phase loops to determine a valid fault location for a phase-ground fault and each of the three phase-phase loops may be used to determine a valid fault location for all the other fault types. It should be noted that the fault location mentioned in the embodiments described above pertains to per unit fault location, but this output can be used to calculate the actual fault location in miles or kilometers if the total line length is mentioned. Thus, technical effects of the present disclosure include systems and methods for using incremental quantities to determine fault location. 
     The present system and method have advantages over existing technology. First, no sequence quantities required for fault location computation in the present system. This helps with systems containing IBRs (Inverter Based Resources), where a reliable negative sequence current is unavailable. Second, the present system and method eliminate dependency of zero sequence incremental loop compensated current and hence, zero sequence impedance. Indeed, all 6 loops can be used but it was observed that the phase-ground loops had a higher error. This is because zero sequence impedance is seldom accurately known. Moreover, the present system and method are applicable to both instantaneous and filtered incremental quantities, but using instantaneous signals instead of filtered signals eliminates the longer filtering delays associated with them. Additionally, the present system and method is also a good alternative for travelling-wave (TW) fault location method for faults occurring near a point-on-wave zero and if the line is terminated with a high impedance element as it becomes a challenge to measure the current TW for such systems. Furthermore, fault type identification is not necessary in the present system and method, which avoids errors associated or challenges faced by fault identification methods. And there are only three phase-to-phase loops are used for fault location computation and a reliable fault location result can be obtained in just over a power system cycle. 
     After the fault and its location are determined, the computing system may send commands to related devices (e.g., contactors, relays, circuit breakers) to adjust operations based on the fault location at block  166 . For example, the operations might include a protective action, which may include opening or closing a circuit breaker, selectively isolating a portion of the electric power system via the breaker, etc. In various embodiments, the protective action may involve coordinating protective actions with other devices in communication with the system  100 . In addition, the fault location computation can be used during post-processing actions to provide more visibility into the system like system parameters. 
     Furthermore, some depictions of logic circuitry have been described via this disclosure. It should be understood that logically-equivalent circuitry may be used herein to implement the systems and methods described. For example, a logical XOR gate may be replaced via a logically-equivalent combination of NOT gates, AND gates, Inverse NOT gates, OR gates, NAND gates, NOR gates, or the like. 
     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 precise 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 or may not include long-distance transmission of high-voltage power. 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 disclosure should, therefore, be determined only by the following claims. 
     Indeed, the embodiments set forth in the present disclosure may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and have been described in detail herein. However, it may be understood that the disclosure is not intended to be limited to the particular forms disclosed. The disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the disclosure as defined by the following appended claims. In addition, the techniques presented and claimed herein are referenced and applied to material objects and concrete examples of a practical nature that demonstrably improve the present technical field and, as such, are not abstract, intangible or purely theoretical. Further, if any claims appended to the end of this specification contain one or more elements designated as “means for [perform]ing [a function] . . . ” or “step for [perform]ing [a function] . . . ”, it is intended that such elements are to be interpreted under 35 U.S.C. 112(f). For any claims containing elements designated in any other manner, however, it is intended that such elements are not to be interpreted under 35 U.S.C. 112(f).