Distance protection for power systems based on matched apparent impedance

Abstract

The present disclosure relates to a method for controlling a protection system for a power system including a transmission line terminated by a first terminal coupled to a first power source and a second terminal coupled to a second power source, the method including: obtaining a plurality of voltage measurements and a plurality of current measurements at the first terminal; determining phase angle boundaries of a fault current based on the plurality of voltage measurements and the plurality of current measurements; determining a first apparent impedance based on a first phase angle within the phase angle boundaries or at one of the phase angle boundaries originating from the first terminal; determining a second apparent impedance based on a second phase angle within the phase angle boundaries or at one of the phase angle boundaries originating from the first terminal; determining a third apparent impedance and a fourth apparent impedance originating from the first terminal based on the first apparent impedance and the second apparent impedance; and controlling the protection system based on the third apparent impedance and the fourth apparent impedance. The present disclosure also relates to respective devices and computer-readable media.

Description

[Technical Field]

[0001] Technical Field The present disclosure relates to a method, a device, a computer-readable medium, and a power system for controlling a protection system for a power system including a transmission line. [Background technology]

[0002] background Renewable energy generators, including solar and wind turbine generators, are referred to as power electronics or inverter-based resources (IBRs) because they are fully or partially connected to the grid via power electronic converters. Due to their different structures and control strategies, IBRs have different fault characteristics than conventional synchronous generators (SGs). Grid codes and fault ride-through (FRT) requirements modulate the voltage and current output of IBRs during faults. This poses challenges to traditional protective relaying principles designed for SG-dominated grids.

[0003] Protection systems in power systems with transmission networks are traditionally dominated by staged distance protection, with three zones providing primary and backup protection in a coordinated fashion. Distance protection, also known as impedance protection, is based on the principle that impedance measured at the terminals using local voltages and currents indicates the location of a fault. FIG. 1 shows a two-port equivalent model of a power system 100 with a transmission line 130. The transmission line is terminated at a first end by a first terminal, or bus "M," 110, coupled to a first power source 111 and at a second end by a second terminal, or bus "N," 120, coupled to a second power source 121. The source impedance of the first power source 111 is represented by a first source impedance Z, which is coupled in series with the first power source 111 and the bus "M" 110. sM112, and the source impedance of the second power supply 121 is modeled as a source impedance Z sN 122. The line segment between bus "M" 110 and bus "N" 120 during a fault occurring at fault location "F", hereafter also referred to as segment "MN", is modeled as dZ 1L , (1-d)Z 1L , and R F Hereinafter, the first source 111 will also be referred to as the local source 111, and the second source 121 will also be referred to as the remote source 121. The power system 100 further comprises a relay "R" 140 which may be mounted at, in, or on, or associated with, the terminal bus "M" 110. The relay "R" 140 may comprise measurement devices, in particular current and potential transformers (CTs and PTs), which measure the voltage and current of the bus "M" 110. The voltage and current of the bus "M" 110 may also be obtained in other ways, for example by other measurement means.

[0004] For a fault at location "F" on segment "MN", the measured apparent impedance seen by bus "M" looking into segment "MN" may be determined as follows:

[0005]

number

[0006]

number

[0007]

number

[0008] Therefore, it may be appreciated that the performance of the first approach is affected when applied to IBR-connected transmission lines. Existing distance protection principles designed for SG-connected lines operate accurately because the SG-connected system is uniform. The controlled power electronic converter-based current contribution from the IBR introduces non-uniformity, causing erroneous apparent impedance calculations. The error is higher for faults with higher fault tolerance. The apparent impedance error can be inductive or capacitive in nature depending on the phase angle of the IBR output current, thus causing the distance relay to overreach or underreach. Summary of the Invention [Problem to be solved by the invention]

[0009] overview Therefore, there is a need for improved methods, devices, and computer-readable media for controlling protection systems for power systems. [Means for solving the problem]

[0010] The present disclosure relates to a method for controlling a protection system for a power system including a transmission line terminated by a first terminal coupled to a first power source and by a second terminal coupled to a second power source, the method including obtaining a plurality of voltage measurements and a plurality of current measurements at the first terminal; determining phase angle boundaries of a fault current based on the plurality of voltage measurements and the plurality of current measurements; determining a first apparent impedance based on a first phase angle within the phase angle boundary or at one of the phase angle boundaries originating from the first terminal; determining a second apparent impedance based on a second phase angle within the phase angle boundary or at one of the phase angle boundaries originating from the first terminal; determining a third apparent impedance and a fourth apparent impedance originating from the first terminal based on the first apparent impedance and the second apparent impedance; and controlling the protection system based on the third apparent impedance and the fourth apparent impedance.

[0011] According to one embodiment, the phase angle boundary of the fault current is determined based on the phase angle of the fault current, where the phase angle of the fault current depends on the fault location, the fault current is a complex number, and the phase angle of the fault current is the angle, phase, or argument of the fault current measured specifically during the fault.

[0012] According to one embodiment, the phase angle boundaries are or include minimum and maximum phase angles of the fault current for a fault occurring within the segment of the transmission line between the first terminal and the second terminal.

[0013] According to one embodiment, the first phase angle is determined based on a first parameter, in particular a preset distance between the first terminal and a first position on the transmission line, and the second phase angle is determined based on a second parameter, in particular a preset distance between the first terminal and a second position on the transmission line different from the first position.

[0014] According to one embodiment, the first phase angle is a minimum phase angle of the fault current and the second phase angle is a maximum phase angle of the fault current.

[0015] According to one embodiment, the method further includes determining a source impedance of the second power source based on the plurality of voltage measurements and the plurality of current measurements at the first terminal, wherein determining the first apparent impedance and determining the second apparent impedance are based on the source impedance of the second power source.

[0016] According to one embodiment, the source impedance of the second power source is determined based on a plurality of voltage measurements and a plurality of current measurements taken before the fault instance.

[0017] According to one embodiment, the first power source is one of a grid, a synchronous power source, a non-conventional power source, in particular an inverter-based resource, and the second power source is a synchronous power source or a grid having at least one synchronous power source and / or at least one non-conventional power source.

[0018] According to one embodiment, the method further includes determining an impedance of the first power source after the fault instance based on a plurality of voltage measurements and a plurality of current measurements obtained before and after the fault instance, and determining the first apparent impedance and the second apparent impedance is based on the impedance of the first power source.

[0019] According to one embodiment, determining the third apparent impedance and the fourth apparent impedance is or includes summing the first apparent impedance and the second apparent impedance, in particular linearly, more particularly with a first weight that scales the first apparent impedance and a second weight that scales the second apparent impedance, the first weight being different from the second weight.

[0020] According to one embodiment, the method further includes determining a fifth apparent impedance based on the third apparent impedance and the fourth apparent impedance, in particular based on a first ratio of the third apparent impedance to a line impedance of the transmission line and a second ratio of the fourth apparent impedance to the line impedance of the transmission line, and the protection system is controlled based on the fifth apparent impedance.

[0021] According to one embodiment, at least one voltage measurement of the plurality of voltage measurements of the first terminal is measured before the fault instance, and / or at least one voltage measurement of the plurality of voltage measurements of the first terminal is measured after the fault instance.

[0022] According to one embodiment, at least one current measurement value of the plurality of current measurements of the first terminal is measured before the fault instance, and / or at least one current measurement value of the plurality of current measurements of the first terminal is measured after the fault instance.

[0023] The present disclosure also relates to a device for controlling a protection system for a power system including a transmission line terminated by a first terminal coupled to a first power source and by a second terminal coupled to a second power source, the device comprising: a processor configured to obtain a plurality of voltage measurements and a plurality of current measurements at the first terminal; determine a phase angle boundary of a fault current based on the plurality of voltage measurements and the plurality of current measurements; determine a first apparent impedance based on a first phase angle within the phase angle boundary or at one of the phase angle boundaries originating from the first terminal; determine a second apparent impedance based on a second phase angle within the phase angle boundary or at one of the phase angle boundaries originating from the first terminal; determine a third apparent impedance and a fourth apparent impedance originating from the first terminal based on the first apparent impedance and the second apparent impedance; and control the protection system based on the third apparent impedance and the fourth apparent impedance.

[0024] According to one embodiment, the processor is further configured to perform the method of any one of the above-mentioned embodiments.

[0025] The present disclosure also relates to a computer-readable medium carrying instructions for performing the method of any one of the above-mentioned embodiments for controlling a protection system for an electric power system.

[0026] The present disclosure further relates to a power system comprising a transmission line, a device of any one of the above-mentioned embodiments, and a computer-readable medium of any one of the above-mentioned embodiments.

[0027] Various exemplary embodiments of the present disclosure are directed to providing features that will become readily apparent by reference to the following description in conjunction with the accompanying drawings. In accordance with various embodiments, exemplary systems, methods, and devices are disclosed herein. It is understood, however, that these embodiments are presented by way of example and not limitation, and it will be apparent to those skilled in the art upon reading this disclosure that various modifications to the disclosed embodiments can be made while remaining within the scope of the present disclosure.

[0028] Thus, the present disclosure is not limited to the example embodiments and applications described and illustrated herein. Additionally, the specific order and / or hierarchy of steps in the methods disclosed herein is merely exemplary approaches. Based on design preferences, the specific order or hierarchy of steps in a disclosed method or process can be rearranged while remaining within the scope of the present disclosure. Thus, those skilled in the art will understand that the methods and techniques disclosed herein present various steps or operations in a sample order, and that the present disclosure is not limited to the specific order or hierarchy presented, unless otherwise stated.

[0029] Hereinafter, exemplary embodiments of the present disclosure will be described. It should be noted that some aspects of any one of the described embodiments may also be found in some other embodiments, unless otherwise specified or obvious. However, for the purpose of improving comprehension, each aspect will be described in detail only when first mentioned, and repeated descriptions of the same aspects will be omitted.

[0030] These and other aspects and their implementations are described in more detail in the drawings, description, and claims. [Brief explanation of the drawings]

[0031] [Figure 1] A two-port equivalent model of a power system, especially a network, with transmission lines is presented. [Figure 2a)]A method for calculating apparent impedance is presented. [Figure 2b] A method for calculating apparent impedance is presented. [Figure 3a)] FIG. 2 shows the apparent impedance angle difference and apparent impedance trajectory calculated according to the disclosed method. [Figure 3b)] FIG. 2 shows the apparent impedance angle difference and apparent impedance trajectory calculated according to the disclosed method. [Figure 4] FIG. 2 shows the numerical performance of apparent impedance calculated according to the disclosed method. [Figure 5] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 6a)] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 6b] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 7] 1 illustrates a power system, particularly a network, including a non-traditional power source according to one embodiment of the present disclosure. [Figure 8] 1 shows a graphical representation of the range of apparent impedance calculated according to one embodiment of the present disclosure. [Figure 9] 1 illustrates a power system, particularly a network, including a non-traditional power source according to one embodiment of the present disclosure. [Figure 10a)] 1 shows measurements at the connection point and source impedance of a remote power supply during a single event in a non-conventional power supply. [Figure 10b] 1 shows measurements at the connection point and source impedance of a remote power supply during a single event in a non-conventional power supply. [Figure 10c)] 1 shows measurements at the connection point and source impedance of a remote power supply during a single event in a non-conventional power supply. [Figure 10d)] 1 shows measurements at the connection point and source impedance of a remote power supply during a single event in a non-conventional power supply. [Figure 10e)]1 shows measurements at the connection point and source impedance of a remote power supply during a single event in a non-conventional power supply. [Figure 11a)] 1 illustrates the source impedance of a remote power supply during multiple events in a non-traditional power supply. [Figure 11b)] 1 illustrates the source impedance of a remote power supply during multiple events in a non-traditional power supply. [Figure 11c)] 1 illustrates the source impedance of a remote power supply during multiple events in a non-traditional power supply. [Figure 11d)] 1 illustrates the source impedance of a remote power supply during multiple events in a non-traditional power supply. [Figure 12] 10 shows a summary of numerical results for apparent impedance calculated according to various methods, including a method according to one embodiment of the present disclosure. [Figure 13] 1 shows a graphical representation of apparent impedance calculated according to various methods, including a method according to an embodiment of the present disclosure. [Figure 14] 10 shows a summary of numerical results for apparent impedance calculated according to various methods, including a method according to one embodiment of the present disclosure. [Figure 15] 1 shows a graphical representation of apparent impedance calculated according to various methods, including a method according to an embodiment of the present disclosure. [Figure 16a)] 1 illustrates a device, a computer-readable medium, and a power system according to one embodiment of the present disclosure. [Figure 16b)] 1 illustrates a device, a computer-readable medium, and a power system according to one embodiment of the present disclosure. [Figure 16c)] 1 illustrates a device, a computer-readable medium, and a power system according to one embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0032] Detailed Description of Disclosure 5 shows a flowchart of a method according to one embodiment of the present disclosure. At S501, multiple voltage measurements and multiple current measurements of a first terminal are obtained. At S502, a phase angle boundary of a fault current is determined based on the multiple voltage measurements and multiple current measurements. At S503, a first apparent impedance is determined based on a first phase angle within or at one of the phase angle boundaries originating from the first terminal. At S504, a second apparent impedance is determined based on a second phase angle within or at one of the phase angle boundaries originating from the first terminal. At S505, a third apparent impedance and a fourth apparent impedance originating from the first terminal are determined based on the first apparent impedance and the second apparent impedance. At S506, a protection system is controlled based on the third apparent impedance and the fourth apparent impedance.

[0033] A protection system may be a system that detects faults or abnormal operating conditions and initiates corrective action. A protection system may be distance protection for transmission lines in an electric power system.

[0034] A transmission line may be a cable or other structure that carries electrical energy in an electrical power system, particularly by conducting electromagnetic waves.

[0035] The terminal may be an electrical connector that terminates a first electrical cable and connects to a second electrical cable, thereby transmitting electrical current therebetween.

[0036] Phase angle boundaries may be limits on phase angles that describe the minimum and maximum values of the angle, phase, or argument of a complex number or phase shift between two signals.

[0037] A fault current may be the current that flows through a circuit during an electrical fault condition. The apparent impedance may be the ratio between the voltage and the current at the injection point of the circuit.

[0038] The source impedance may be the impedance, especially the equivalent impedance, of the source, especially the power source.

[0039] A failure instance may be a time instance when a failure occurs. According to one embodiment, the phase angle boundary of the fault current is determined based on the phase angle of the fault current, where the phase angle of the fault current depends on the fault location, the fault current is a complex number, and the phase angle of the fault current is the angle, phase, or argument of the fault current measured specifically during the fault.

[0040] According to one embodiment, the plurality of voltage measurements and the plurality of current measurements include or are measurements of multiple phases, in particular three phases, transmitted over the transmission line.

[0041] According to one embodiment, the method illustrated in FIG. 5 is applicable to all fault types, including, among others, single phase-to-ground faults, phase-to-phase faults, phase-to-ground faults, and three phase-to-ground faults.

[0042] FIG. 6 illustrates a flowchart of a method according to one embodiment of the present disclosure. The flowchart of FIG. 6 considers, and therefore references, the exemplary power system 700 of FIG. 7. The power system 700 includes a protected power line 730 terminated by a first terminal, i.e., bus "M" 710, coupled to a first power source, i.e., IBR system 711, and by a second terminal, i.e., bus "N" 720, coupled to a second power source, i.e., grid 721. The first terminal is merely an exemplary component for illustrative purposes, and it will be understood by those skilled in the art that the protected power line may be terminated by means other than the first terminal. Likewise, it will be understood by those skilled in the art that the second terminal is merely an exemplary component for illustrative purposes, and the protected power line may be terminated by means other than the second terminal.

[0043] An electric power system may be a network of power devices coupled via transmission lines for power transmission. A power device may be a power source, a power consumer, or a grid. A power source may be an electrical device that supplies electrical energy to an electrical load, particularly by converting one form of energy to another. A power source may be a synchronous or asynchronous generator, also known as a non-conventional power source.

[0044] The source impedance of the second power supply 721 is a second source impedance Z G722. The first power source may be any other non-conventional power source, i.e., a non-conventional power source other than an IBR, a synchronous power source, or a grid including non-conventional and / or synchronous power sources. The non-conventional power source may correspond to an asynchronous power source including an IBR. The second power source may be a synchronous power source or a grid including synchronous and / or non-conventional power sources. According to one embodiment, the first power source is one of a grid, a synchronous power source, or a non-conventional power source, particularly an inverter-based resource, and the second power source is a synchronous power source or a grid having at least one synchronous power source and / or at least one non-conventional power source. Although omitted for simplicity, power system 700 may further include a relay "R" that may be mounted at, within, or on or associated with terminal bus "M" 710. Relay "R" may include measuring devices, particularly current and potential transformers (CTs and PTs), that measure voltages and currents of bus "M" 710. The voltage and current of bus "M" 710 may also be obtained in other ways, such as by other measurement means. The power system 700 may further include devices, particularly intelligent electronic devices (IEDs), that may be mounted on, in, or on, or associated with, the terminal bus "M" 710. The IED may be a relay "R." The IED may be a computer-readable device configured to perform the method of the embodiment shown in FIG. 6. With reference to FIG. 6, the first power source, the second power source, and the second source impedance are hereinafter referred to as the IBR system, the grid-side power source, and the grid-side source impedance.

[0045] According to one embodiment, at least one voltage measurement of the plurality of voltage measurements of the first terminal is measured before the fault instance, and / or at least one voltage measurement of the plurality of voltage measurements of the first terminal is measured after the fault instance.

[0046] According to one embodiment, at least one current measurement value of the plurality of current measurements of the first terminal is measured before the fault instance, and / or at least one current measurement value of the plurality of current measurements of the first terminal is measured after the fault instance.

[0047] The embodiment of FIG. 6 includes two parts: (i) a pre-fault analysis 620 of grid-side source impedance as shown in FIG. 6b), and (ii) a post-fault analysis 630 for calculating a corrected apparent impedance as seen by bus "M" 710 as shown in FIG. 6a). Data, e.g., voltage and / or current measurements of bus "M" 710, are acquired at 610. In the pre-fault analysis 620, a grid-side equivalent source impedance 722 is evaluated and estimated based on acquired data 612 obtained before the fault, as detected at 614. An output grid-side source impedance 628 is provided to the post-fault analysis 630 for use in calculating a corrected apparent impedance as seen by bus "M" 710 in the event of a fault. A detailed description of the pre-fault analysis 620 and post-fault analysis 630 is provided below.

[0048] Pre-fault analysis of grid-side source impedance 620: An IBR event is detected at 621 based on acquired data 612, particularly voltage and current measurements at the first terminal, and / or the negative output 616 of the fault detection at 614, i.e., when no fault is detected. An event can be any change in the IBR system 711 that results in a change in the power injected from the IBR system 711 into the network. According to one embodiment, in a wind park, events may include the stopping / starting of wind turbine units, changes in wind speed, cut-in / cut-out events, etc. Step-by-step investigations by intentionally modifying the inverter current reference may also be used. As a result, the current injected by the IBR into the grid through the connecting power lines may change instantaneously. Such step-by-step events may be used to estimate grid-side equivalent parameters. Reliable events may be identified at 622 based on changes in power, voltage, and / or current bus "M" 710, particularly by comparing parameters to specific threshold levels. Such changes may also be correlated with an event flag / signal communicated from the IBR side, particularly if communication exists between the IBR side and a connection point, e.g., bus "M." According to one embodiment, a change in the electrical parameters of voltage, current, and / or power observed on bus "M" 710 and a concurrent change in wind speed indicated by the park's anemometer readings can be used as a reliable IBR event.

[0049] A change in the current injection from bus "M" 710 onto the protected transmission line 730 may be thought of as a change in the current injected at bus "N" 720 via the protected transmission line 730. This change in injected current induces a change in the voltage at bus "N" 720. While voltage and current measurements of bus "M" 710 may be obtained, the voltage and current parameters at bus "N" 720 are not readily available in the absence of a dedicated communication link between bus "M" 710 and bus "N" 720. However, the voltage and current parameters at bus "N" 720 may be calculated at 623 from the available voltage and current measurements of bus "M" 710 as follows:

[0050]

number

[0051]

number

[0052]

number

[0053]

number

[0054] Both the calculation and estimation procedures described above may be implemented on a window of data after the IBR event. For example, a 0.2-second long data window after the IBR event may be selected. An estimation of the grid-side source impedance 722 may be performed for each data point within the window. A final estimate for that data window may be obtained as an average of the estimates obtained for each data point. In doing so, the grid-side source impedance estimate 628 may be obtained based, and particularly only based, on measurements available on bus "M" 710 and included in the process for accurate calculation of the apparent impedance seen by bus "M" 710, particularly corrected for the transmission lines connecting the IBR system 711.

[0055] Post-failure analysis 630 (reach factors): Post-fault analysis 630 takes measurements, particularly voltage and current measurements of bus "M" 710 taken before and after the fault occurrence instance, as well as an estimate of the grid-side source impedance 628. After fault detection in 614, the measured apparent impedance Z Ris calculated in 631 according to equation (8). Note that the term "fault detection" in distance relaying can mean the identification of a fault event from normal load conditions based on voltage and / or current measurements. Reach may be the apparent impedance measured by a relay, in the case of a fault, at a measurement location on the transmission line or in the terminal terminating the transmission line. Underreach may be when a relay measures more impedance, in particular the apparent impedance seen by the relay, than the actual value, which may cause the relay to not operate for zone faults. Overreach may be when a relay measures less impedance, in particular the apparent impedance seen by the relay, than the actual value, which may cause the relay to operate for out-of-zone faults.

[0056]

number

[0057]

number

[0058]

number

[0059] where CDF represents the current distribution coefficient and is given as:

[0060]

number

[0061]

number

[0062]

number

[0063] At 633, the two CDFs may be calculated as follows:

[0064]

number

[0065] For each of the above CDFs, the two angles of the fault current are obtained as follows:

[0066]

number

[0067] According to one embodiment, the phase angle boundaries are or include minimum and maximum phase angles of the fault current for a fault occurring within the segment of the transmission line between the first terminal and the second terminal.

[0068] According to one embodiment, the first phase angle is determined based on a first parameter, in particular a preset distance between the first terminal and a first position on the transmission line, and the second phase angle is determined based on a second parameter, in particular a preset distance between the first terminal and a second position on the transmission line different from the first position.

[0069] According to one embodiment, the first phase angle is a minimum phase angle of the fault current and the second phase angle is a maximum phase angle of the fault current.

[0070]

number

[0071]

number

[0072]

number

[0073]

number

[0074] According to one embodiment, the method further includes determining a source impedance of the second power source based on the plurality of voltage measurements and the plurality of current measurements at the first terminal, wherein determining the first apparent impedance and determining the second apparent impedance are based on the source impedance of the second power source.

[0075] According to one embodiment, the source impedance of the second power source is determined based on a plurality of voltage measurements and a plurality of current measurements taken before the fault instance.

[0076] According to one embodiment, the method further includes determining an impedance of the first power source after the fault instance based on a plurality of voltage measurements and a plurality of current measurements obtained before and after the fault instance, and determining the first apparent impedance and the second apparent impedance is based on the impedance of the first power source.

[0077]

number

[0078] According to one embodiment, determining the third apparent impedance and the fourth apparent impedance is or includes summing the first apparent impedance and the second apparent impedance, in particular linearly, more particularly with a first weight that scales the first apparent impedance and a second weight that scales the second apparent impedance, the first weight being different from the second weight.

[0079]

number

[0080] According to one embodiment, the method further includes determining a fifth apparent impedance based on the third apparent impedance and the fourth apparent impedance, in particular based on a first ratio of the third apparent impedance to a line impedance of the transmission line and a second ratio of the fourth apparent impedance to the line impedance of the transmission line, and the protection system is controlled based on the fifth apparent impedance.

[0081]

number

[0082] Pre-fault analysis (grid-side source impedance estimation): For illustrative purposes, the grid-side source impedance is maintained as 15∠84° ohms. The following are shown: (i) a calculation of the grid-side source impedance during an IBR event using ideal measurements for a single IBR event, calculated in 624, and (ii) an estimation of the grid-side source impedance for multiple IBR events using noisy measurements, calculated in 625. The percentage thresholds for changes in the measured parameters of bus "M" 910 are considered to be 0.2% for voltage, 5% for current, and 5% for power to trigger the calculation / estimation procedure. FIG. 10 shows the measurements and grid-side source impedance at bus "M" 910 during a single event for the non-conventional power source disclosed in FIG. 9. In particular, FIGS. 10a), 10b, and 10c show the percentages of voltage, current, and power measured at POC bus "M" 910 during a wind speed change event that occurred in the IBR system 911. Figures 10d) and 10e) show the magnitude and angle of the grid-side source impedance. The estimated values are calculated according to equations (4) and (5). The average magnitude of the estimated grid-side source impedance is approximately 14.76 Ω (1.6% error), and the average phase angle of the estimated grid-side source impedance is approximately 83.8° (0.2% error).

[0083] Figure 11 shows the source impedance of the remote power source during multiple events for the nonconventional power source disclosed in Figure 9 under noisy measurement conditions. In particular, Figures 11a) and 11b) show the magnitude and angle of the grid-side source impedance for a single IBR event. The estimates are calculated according to Equations (4) through (5). The average magnitude of the estimated grid source impedance is approximately 13.68 Ω (8.8% error), and the average phase angle of the estimated grid source impedance is approximately 89.56° (6.6% error). Figures 11c) and 11d) show the magnitude and angle of the grid-side source impedance from three IBR events. The estimates are calculated based on the least-squares estimation procedure of Equation (6) using measurements from a set of three wind speed change events. The average magnitude of the estimated grid-side source impedance is approximately 14.86 Ω (0.9% error), and the average phase angle of the estimated grid-side source impedance is approximately 84.64° (0.8% error). Thus, an overall improvement in estimation accuracy is observed.

[0084] Post-fault analysis (final corrected apparent impedance calculation): A distance relay (IED) at bus "M" 910 and two fault scenarios are considered. In scenario 1, the grid-side source impedance is considered uniform relative to the line impedance and is maintained at 15° 84° ohms. The fault is simulated at a distance of 90 km from bus "M". In scenario 2, the grid-side source impedance is considered non-uniform and is maintained as 15° 65° ohms. The fault is simulated at a length of 75 km from bus "M". In each of these cases, the fault is considered to be an arc with a resistance of 10 ohms. The relay at bus "M" should not detect the Scenario 1 fault in its Zone 1, but should preferably detect the Scenario 2 fault in Zone 1.

[0085] Scenario 1:

[0086]

number

[0087] Scenario 2:

[0088]

number

[0089] FIG. 16 illustrates a device, a computer-readable medium, and a power system according to one embodiment of the disclosure.

[0090] Device 1610 is a device for controlling a protection system for a power system including a transmission line terminated by a first terminal coupled to a first power source and by a second terminal coupled to a second power source, the device comprising a processor configured to: obtain multiple voltage measurements and multiple current measurements at the first terminal; determine a phase angle boundary of a fault current based on the multiple voltage measurements and multiple current measurements; determine a first apparent impedance based on a first phase angle within the phase angle boundary or at one of the phase angle boundaries originating from the first terminal; determine a second apparent impedance based on a second phase angle within the phase angle boundary or at one of the phase angle boundaries originating from the first terminal; determine a third apparent impedance and a fourth apparent impedance originating from the first terminal based on the first apparent impedance and the second apparent impedance; and control the protection system based on the third apparent impedance and the fourth apparent impedance.

[0091] According to one embodiment, the processor is further configured to perform the method of any one of the above-mentioned embodiments.

[0092] The computer readable medium 1620 is a device for controlling a protection system for a power system, carrying instructions for performing the method of any one of the above-described embodiments.

[0093] The power system 1600 includes a transmission line 1630, a device 1610 according to any one of the above-mentioned embodiments, and a computer-readable medium 1620 according to any one of the above-mentioned embodiments.

[0094] While various embodiments of the present disclosure have been described above, it should be understood that they are presented by way of example only, and not by way of limitation. Similarly, various figures may depict example architectures or configurations provided to enable those skilled in the art to understand example features and functionality of the present disclosure. However, such persons will understand that the present disclosure is not limited to the example architectures or configurations shown, but can be implemented using a variety of alternative architectures and configurations. Moreover, as will be understood by those skilled in the art, one or more features of one embodiment can be combined with one or more features of another embodiment described herein. Thus, the breadth and scope of the present disclosure should not be limited by any of the above-described example embodiments.

[0095] It is also understood that any reference to elements herein using designations such as "first," "second," etc., generally does not limit the quantity or order of those elements. Rather, these designations may be used herein as a convenient means of distinguishing between two or more elements or instances of an element. Thus, a reference to a first and a second element does not imply that only two elements may be employed or that the first element must in any way precede the second element.

[0096] Additionally, those skilled in the art will understand that information and signals may be represented using any of a variety of different technologies and techniques. For example, the data, instructions, commands, information, signals, bits, and symbols that may be referenced in the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

[0097] Those skilled in the art will further recognize that any of the various illustrative logical blocks, units, processors, means, circuits, methods, and functions described in connection with the aspects disclosed herein may be implemented by electronic hardware (e.g., digital implementations, analog implementations, or a combination of the two), firmware, various forms of program or design code incorporating instructions (which may be referred to herein for convenience as "software" or "software units"), or any combination of these technologies.

[0098] To clearly illustrate this interchangeability of hardware, firmware, and software, various illustrative components, blocks, units, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware, firmware, or software, or a combination of these technologies, depends on the particular application and design constraints imposed on the overall system. Those skilled in the art may implement the described functionality in various ways for each particular application, and such implementation decisions do not depart from the scope of the present disclosure. According to various embodiments, a processor, device, component, circuit, structure, machine, unit, etc. may be configured to perform one or more of the functions described herein. The terms "configured to" or "configured for," as used herein with respect to a specified operation or function, refer to a processor, device, component, circuit, structure, machine, unit, etc. that is physically constructed, programmed, and / or arranged to perform the specified operation or function.

[0099] Furthermore, those skilled in the art will understand that the various example methods, logical blocks, units, devices, components, and circuits described herein can be implemented in or performed by an integrated circuit (IC), which may include a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic device, or any combination thereof. The logical blocks, units, and circuits may further include an antenna and / or transceiver for communicating with various components within a network or device. The general-purpose processor may be a microprocessor, although in the alternative, the processor may be any conventional processor, controller, or state machine. A processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors in conjunction with a DSP core, or any other suitable configuration for performing the functions described herein. If implemented in software, the functions may be stored as one or more instructions or code on a computer-readable medium. Thus, the steps of a method or algorithm disclosed herein can be implemented as software stored on a computer-readable medium.

[0100] Computer-readable media includes both computer storage media and communication media, including any medium that can enable a computer program or code to be transmitted from one place to another. Storage media can be any available medium that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store desired program code in the form of instructions or data structures and that can be accessed by a computer.

[0101] Additionally, memory or other storage devices, as well as communication components, may be employed in embodiments of the present disclosure. It will be appreciated that, for clarity, the above description has described embodiments of the present disclosure with reference to different functional units and processors. However, it will be apparent that any suitable distribution of functionality between different functional units, processing logic elements, or domains may be used without detracting from the present disclosure. For example, functionality illustrated as being performed by separate processing logic elements or controllers may be performed by the same processing logic element or controller. Accordingly, references to specific functional units do not refer to a strict logical or physical structure or organization, but merely to suitable means for providing the described functionality.

[0102] Various modifications to the implementations described in this disclosure will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other implementations without departing from the scope of the present disclosure. Thus, the present disclosure is not intended to be limited to the implementations shown herein but is to be accorded the widest scope consistent with the novel features and principles disclosed herein, as set forth in the following claims.

Claims

1. 1. A method for controlling a protection system for an electrical power system comprising a transmission line terminated by a first terminal coupled to a first power source and by a second terminal coupled to a second power source, the method comprising: obtaining a plurality of voltage measurements and a plurality of current measurements at the first terminal; determining a phase angle boundary of a fault current based on the plurality of voltage measurements and the plurality of current measurements; determining a first apparent impedance based on a first phase angle within the phase angle boundary or at one of the phase angle boundaries starting from the first terminal; determining a second apparent impedance based on a second phase angle within the phase angle boundary or at one of the phase angle boundaries originating from the first terminal; determining a third apparent impedance and a fourth apparent impedance originating from the first terminal based on the first apparent impedance and the second apparent impedance; controlling the protection system based on the third apparent impedance and the fourth apparent impedance; A method comprising:

2. 2. The method of claim 1, wherein the phase angle boundaries are or include minimum and maximum phase angles of the fault current for faults occurring in a segment of the transmission line between the first terminal and the second terminal.

3. 3. The method according to claim 1, wherein the first phase angle is determined based on a first parameter, in particular a preset distance between the first terminal and a first position on the transmission line, and the second phase angle is determined based on a second parameter, in particular a preset distance between the first terminal and a second position on the transmission line different from the first position.

4. The method of any one of claims 1 to 3, wherein the first phase angle is the minimum phase angle of the fault current and the second phase angle is the maximum phase angle of the fault current.

5. 5. The method of claim 1, further comprising determining a source impedance of the second power source based on the plurality of voltage measurements and the plurality of current measurements at the first terminal, wherein the determination of the first apparent impedance and the determination of the second apparent impedance are based on the source impedance of the second power source.

6. The method of claim 5 , wherein the source impedance of the second power source is determined based on the plurality of voltage measurements and the plurality of current measurements taken before a fault instance.

7. 7. The method of claim 1, wherein the first power source is one of a grid, a synchronous power source, a non-conventional power source, in particular an inverter-based resource, and the second power source is a synchronous power source or a grid having at least one synchronous power source and / or at least one non-conventional power source.

8. 8. The method of claim 1, further comprising determining an impedance of the first power source after the fault instance based on the plurality of voltage measurements and the plurality of current measurements taken before and after the fault instance, wherein determining the first apparent impedance and the second apparent impedance is based on the impedance of the first power source.

9. 9. The method according to claim 1, wherein the determination of the third apparent impedance and the fourth apparent impedance is or comprises summing the first apparent impedance and the second apparent impedance, in particular linearly, more particularly with a first weight that scales the first apparent impedance and a second weight that scales the second apparent impedance, the first weight being different from the second weight.

10. 10. The method according to claim 1, further comprising determining a fifth apparent impedance based on the third apparent impedance and the fourth apparent impedance, in particular based on a first ratio of the third apparent impedance to a line impedance of the transmission line and a second ratio of the fourth apparent impedance to the line impedance of the transmission line, and wherein the protection system is controlled based on the fifth apparent impedance.

11. 11. The method of claim 1, wherein at least one voltage measurement value of the plurality of voltage measurements of the first terminal is measured before a fault instance and / or at least one voltage measurement value of the plurality of voltage measurements of the first terminal is measured after the fault instance.

12. 12. The method of claim 1, wherein at least one current measurement value of the plurality of current measurements of the first terminal is measured before a fault instance and / or at least one current measurement value of the plurality of current measurements of the first terminal is measured after the fault instance.

13. 1. A device for controlling a protection system for an electric power system comprising a transmission line terminated by a first terminal coupled to a first power source and by a second terminal coupled to a second power source, the device comprising: obtaining a plurality of voltage measurements and a plurality of current measurements at the first terminal; determining a phase angle boundary of a fault current based on the plurality of voltage measurements and the plurality of current measurements; determining a first apparent impedance based on a first phase angle within the phase angle boundary or at one of the phase angle boundaries starting from the first terminal; determining a second apparent impedance based on a second phase angle within the phase angle boundary or at one of the phase angle boundaries starting from the first terminal; determining a third apparent impedance and a fourth apparent impedance originating from the first terminal based on the first apparent impedance and the second apparent impedance; and and controlling the protection system based on the third apparent impedance and the fourth apparent impedance. A device comprising a configured processor.

14. The device of claim 13, wherein the processor is further configured to perform the method of any one of claims 2 to 12.

15. A computer readable medium for controlling a protection system for an electric power system, carrying instructions for carrying out the method of any one of claims 1 to 12.

Images