Distance protection for power systems based on adapted apparent impedance

Abstract

The present disclosure relates to a method for controlling a protection system for a power system, the power system comprising a power 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 comprising: obtaining a plurality of voltage measurements and a plurality of current measurements of 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 starting from the first terminal based on a first phase angle within or at one of the phase angle boundaries; determining a second apparent impedance starting from the first terminal based on a second phase angle within or at one of the phase angle boundaries; determining a third apparent impedance and a fourth apparent impedance starting 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 invention further designs a corresponding device and a computer readable medium.

Description

Technical Field

[0001] The present disclosure relates to an electric power system, and a method, an apparatus, and a computer-readable medium for controlling a protection system for the electric power system, the electric power system including a transmission line. Background Art

[0002] Renewable energy generators (including photovoltaic generators and wind turbine generators) are called power electronic devices or inverter-based resources (IBRs) because they are fully or partially connected to the network through power electronic converters. IBRs have different fault characteristics from traditional synchronous generators (SGs) due to different structures and control strategies. Grid guidelines and fault ride-through (FRT) require that the voltage and current output of IBRs be modulated during faults. This in turn challenges traditional relay protection principles that are designed for grids dominated by SGs.

[0003] Protection systems in power systems including transmission networks are traditionally dominated by stepped distance protection, where three zones provide primary and backup protection in a coordinated manner. 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 the fault. Figure 1 A two-port equivalent model of a power system 100 including a transmission line 130 is illustrated. The transmission line is terminated at a first end by a first terminal (i.e., bus 'M' 110) coupled to a first power source 111, and at a second end by a second terminal (i.e., bus 'N' 120) coupled to a second power source 121. The source impedance of the first power source 111 is modeled as a first source impedance Z coupled in series to the first power source 111 and the bus 'M' 110. SM 112, and the source impedance of the second power supply 121 is modeled as the source impedance Z connected in series to the second power supply 121 and the bus 'N' 120 SN 122. During a fault at fault location 'F', the line section between bus 'M' 110 and bus 'N' 120 (hereinafter also referred to as section 'MN') is 1L 、(1-d)Z 1L and R FModeling is performed. Hereinafter, the first source 111 is also referred to as a local source 111, and the second source 121 is also referred to as a remote source 121. The power system 100 further includes a relay 'R' 140, which may be placed at, in, or on, or associated with, the terminal bus 'M' 110. The relay 'R' 140 may include measuring devices, in particular current and voltage transformers (CT&PT), which measure the voltage at the bus 'M' 110 and the current passing through the bus 'M'. The voltage at the bus 'M' 110 and the current passing through the bus 'M' may also or otherwise be obtained, for example by other measurement means.

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

[0005] Among them, V R and I R Represents the predefined voltage and current respectively. V R and I R can be derived from the voltage at bus 'M' 110 and the current through this bus 'M', in particular according to the formula defined for each fault type. When the fault is a bolted short circuit, that is, when the fault resistance R f When the measured apparent impedance Z is zero, R corresponds to (ie is equal to) the faulted line section impedance dZ l , because it is the only impedance opposing the relay current flowing through the fault between bus 'M' 110 and earth potential. Here, 'd' is the unit distance of the fault from bus 'M' 110, and Z l is the impedance of the transmission line 130 .

[0006] However, this is not the case for resistive faults, since the fault point on the transmission line 130 may no longer be at earth potential. R and I R It can be based on the faulty line section impedance dZ 1L , Fault resistance R F , Fault voltage V F , Fault current I F or the current contribution from the remote side bus 'N' 120 to the fault I rem can be related via a more complex relationship. It can be further based on the inclusion of an additional bias term ΔZ R The first method to measure the relay impedance is described as follows:

[0007]

[0008] where ΔZ R is close to a real number, because I F and I R The angles of are close to the same value. This may be true for a grid dominated by synchronous generators, where the power system is mainly homogeneous, i.e., the phase angles of the transmission line 130, the remote source impedance 122, and the local source impedance 112 are very close to each other, such as 0° to 15°, more particularly 5° to 10°. In such cases, ΔZ may be considered within the resistive range of the traditional quadrilateral characteristic R (which may be primarily resistive) to ensure the reliability of protection.

[0009] However, as the penetration of IBR in the grid increases, the power system has become increasingly heterogeneous. When the local source 111 is a non-conventional power source (e.g., IBR), the output current angle is highly modulated from the output current angle obtained when the local source 111 is a synchronous source, and thus I F with I R The difference between the angles may no longer be small (e.g. The non-conventional power supply can be equivalent to an asynchronous power supply including an IBR. Therefore, the term in equation (2) can have a larger angle, and the deviation impedance term ΔZ R It may no longer be resistive in nature. This causes large errors in the apparent resistance and reactance calculated according to the first method. FIG2 illustrates a method for calculating apparent impedance, in particular the first method. In particular, Figure 2a )and Figure 2b ) respectively illustrate the apparent impedance Z on the complex plane when the deviation impedance is inductive and capacitive R With the fault resistance R F The error increases as the error increases. This is demonstrated below using an illustrative failure case.

[0010] Illustrative case: Zone 1 phase A to ground (Ag) fault on segment 'MN': The Ag fault is at a distance of 20% from bus 'M' 110 on segment 'MN' (ie, d = 0.2 pu), and R F =20Ω. The apparent impedance Z can be calculated as follows R :

[0011]

[0012] Among them, V AM and I AMare the phase A voltage and current phasors at bus 'M' 110, I0 is the zero sequence current at bus 'M' 110, and R F is the fault resistance. dZ 1L It can be the line impedance Z up to the fault point F . Figure 3a ) shows the fault current I F and relay current (I AM +K0I0) Figure 3b ) show apparent impedance trajectory graphs. For comparison purposes, these graphs include data points measured when the first power source is an IBR, and additional data points measured when the first power source is a synchronous generator having the same capacity as the IBR, thereby replacing the IBR.

[0013] As from Figure 3a ) shows that, when compared with the SG-connected system (approximately -50°), for the IBR-connected system, the The absolute value of is higher (approximately -60°). Substituting the variables into equation (3) for the IBR-connected system and the SG-connected system yields the apparent impedance calculated according to the first method, as Figure 4 The actual fault impedance is 0.71+10.15i. The calculated apparent impedances are 22.83+8.32i and 13.83-6.84i for the SG-connected system and the IBR-connected system, respectively. In this case, the reactance shift is -16.99Ω for the IBR-connected system, compared to -1.83Ω for the SG-connected system.

[0014] Therefore, one can understand that the performance of the first approach is affected when applied to IBR-connected transmission lines. Since the SG-connected system is homogeneous, the existing distance protection concept designed for SG-connected lines operates accurately. The current contribution based on the controlled power electronic converter from the IBR produces non-homogeneity and causes incorrect apparent impedance calculation. For faults with higher fault resistance, the error is higher. Depending on the phase angle of the IBR output current, the error in the apparent impedance can be inductive or capacitive in nature, and therefore the distance relay can be over-ranged or under-ranged. Summary of the invention

[0015] Therefore, there exists a need for an improved method, apparatus, and computer-readable medium for controlling a protection system for an electric power system.

[0016] The present disclosure relates to a method for controlling a protection system for an electric power system, the electric power system comprising a transmission line, the transmission line being terminated with a first terminal connected to a first power source and a second terminal connected to a second power source, the method comprising: obtaining a plurality of voltage measurements and a plurality of current measurements of 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 starting from the first terminal based on a first phase angle within or at one of the phase angle boundaries; determining a second apparent impedance starting from the first terminal based on a second phase angle within or at one of the phase angle boundaries; determining a third apparent impedance and a fourth apparent impedance starting 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.

[0017] According to an embodiment, the phase angle boundary of the fault current is determined based on the phase angle of the fault current, wherein the phase angle of the fault current depends on the fault location, wherein the fault current is a complex number, and wherein the phase angle of the fault current is the angle, phase or argument of the fault current, in particular measured during the fault.

[0018] According to an embodiment, for a fault occurring in a section of the power transmission line between the first terminal and the second terminal, the phase angle boundary is or comprises a minimum phase angle and a maximum phase angle of the fault current.

[0019] According to an 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 wherein 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, the second position being different from the first position.

[0020] According to an embodiment, the first phase angle is a minimum phase angle of the fault current and wherein the second phase angle is a maximum phase angle of the fault current.

[0021] According to an embodiment, the method further comprises determining a source impedance of the second power source based on the plurality of voltage measurements and the plurality of current measurements of 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.

[0022] According to an embodiment, the source impedance of the second power source is determined based on the plurality of voltage measurements and the plurality of current measurements obtained prior to the fault instance.

[0023] According to an embodiment, the first power source is one of a grid, a synchronous power source, an unconventional power source, in particular an inverter-based resource, and wherein the second power source is a synchronous power source or a grid having at least one synchronous power source and / or at least one unconventional power source.

[0024] According to an embodiment, the method further comprises 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 obtained 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.

[0025] According to an 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 summing, more particularly, summing using a first weight for scaling the first apparent impedance and a second weight for scaling the second apparent impedance, wherein the first weight is different from the second weight.

[0026] According to an embodiment, the method further comprises 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 the line impedance of the transmission line and a second ratio of the fourth apparent impedance to the line impedance of the transmission line, wherein the protection system is controlled based on the fifth apparent impedance.

[0027] According to an embodiment, at least one of the plurality of voltage measurements of the first terminal is measured before the fault instance and / or at least one of the plurality of voltage measurements of the first terminal is measured after the fault instance.

[0028] According to an embodiment, at least one current measurement of the plurality of current measurements of the first terminal is measured before the fault instance and / or at least one current measurement of the plurality of current measurements of the first terminal is measured after the fault instance.

[0029] The present disclosure also relates to a device for controlling a protection system for an electric power system, the electric power system comprising a transmission line, the transmission line being terminated at a first terminal connected to a first power source and a second terminal connected to a second power source, the device comprising a processor, the processor being configured to: obtain a plurality of voltage measurements and a plurality of current measurements of 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 starting from the first terminal based on a first phase angle within or at one of these phase angle boundaries; determine a second apparent impedance starting from the first terminal based on a second phase angle within or at one of these phase angle boundaries; determine a third apparent impedance and a fourth apparent impedance starting 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.

[0030] According to an embodiment, the processor is further configured to perform the method of any one of the embodiments described above.

[0031] The present disclosure also relates to a computer-readable medium for controlling a protection system for an electric power system, the computer-readable medium carrying instructions for executing the method of any one of the embodiments described above.

[0032] The present disclosure further relates to a power system comprising a power transmission line, a device of any one of the embodiments described above, and a computer-readable medium of any one of the embodiments described above.

[0033] Various exemplary embodiments of the present disclosure are directed to providing features that will become apparent by reference to the following description when understood in conjunction with the accompanying drawings. According to various embodiments, exemplary systems, methods, and devices are disclosed herein. However, it should be understood that these embodiments are presented by way of example and not limitation, and it will be apparent to those of ordinary skill in the art who read this disclosure that various modifications may be made to the disclosed embodiments while remaining within the scope of this disclosure.

[0034] Therefore, the present disclosure is not limited to the exemplary embodiments and applications described and illustrated herein. Additionally, the specific order and / or hierarchy of steps in the methods disclosed herein are merely exemplary methods. Based on design preferences, the specific order or hierarchy of steps of the disclosed methods or processes can be rearranged while remaining within the scope of the present disclosure. Therefore, it will be understood by those of ordinary skill in the art that the methods and techniques disclosed herein present various steps or actions in a sample order, and unless otherwise expressly stated, the present disclosure is not limited to the specific order or hierarchy presented.

[0035] Hereinafter, exemplary embodiments of the present disclosure will be described. It should be noted that, unless otherwise stated or apparent, some aspects of any of the described embodiments may also be found in some other embodiments. However, in order to increase understandability, each aspect will be described in detail only when first mentioned, and any repeated description of the same aspect will be omitted.

[0036] The above and other aspects and embodiments thereof are described in more detail in the drawings, the description and the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A two-port equivalent model of an electric power system, in particular a network, including transmission lines is illustrated.

[0038] FIG2 illustrates a method for apparent impedance calculation.

[0039] FIG. 3 illustrates the angle difference of apparent impedance and the apparent impedance locus calculated according to the method disclosed in FIG. 2 .

[0040] Figure 4 The numerical performance of the apparent impedance calculated according to the method disclosed in FIG. 2 is illustrated.

[0041] Figure 5 A flow chart of a method according to an embodiment of the present disclosure is illustrated.

[0042] FIG6 illustrates a flow chart of a method according to an embodiment of the present disclosure.

[0043] Figure 7 An electric power system, in particular a network, including non-conventional power sources according to an embodiment of the present disclosure is illustrated.

[0044] Figure 8 Illustrated is a graphical representation of apparent impedance ranges calculated according to an embodiment of the present disclosure.

[0045] Fig. 9 An electric power system, in particular a network, including non-conventional power sources according to an embodiment of the present disclosure is illustrated.

[0046] FIG. 10 illustrates the measured values ​​and source impedance of a remote power supply at a connection point during a single event in an unconventional power supply.

[0047] FIG. 11 illustrates the source impedance of a remote power supply during multiple events occurring in an unconventional power supply.

[0048] Fig.12 A summary of numerical results of apparent impedance calculated according to various methods, including a method according to an embodiment of the present disclosure, is illustrated.

[0049] Fig.13Illustrated are graphical representations of apparent impedance calculated according to various methods, including methods according to embodiments of the present disclosure.

[0050] Fig.14 A summary of numerical results of apparent impedance calculated according to various methods, including a method according to an embodiment of the present disclosure, is illustrated.

[0051] Fig.15 Illustrated are graphical representations of apparent impedance calculated according to various methods, including methods according to embodiments of the present disclosure.

[0052] FIG. 16 illustrates an apparatus, a computer-readable medium, and a power system according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0053] Figure 5 A flow chart of a method according to an embodiment of the present disclosure is illustrated. At S501, a plurality of voltage measurements and a plurality of current measurements of a first terminal are obtained. At S502, a phase angle boundary of a fault current is determined based on the plurality of voltage measurements and the plurality of current measurements. At S503, a first apparent impedance starting from the first terminal is determined based on a first phase angle within or at one of the phase angle boundaries. At S504, a second apparent impedance starting from the first terminal is determined based on a second phase angle within or at one of the phase angle boundaries. At S505, a third apparent impedance and a fourth apparent impedance starting 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.

[0054] 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 within an electric power system.

[0055] A transmission line may be a cable or other structure in an electric power system that carries electrical energy, particularly by conducting electromagnetic waves.

[0056] The terminal may be an electrical connector that terminates a first electrical cable and connects to a second electrical cable, thereby transferring electrical current from / between them.

[0057] Phase angle boundaries may be phase angle limits that describe minimum and maximum values ​​of a complex angle, phase, argument, or phase shift between two signals.

[0058] Fault current may be the current that flows through a circuit during an electrical fault condition.

[0059] Apparent impedance may be the ratio of voltage to current in a circuit's injection point.

[0060] The source impedance may be the impedance, in particular the equivalent impedance, of a source, in particular a power supply.

[0061] A failure instance may be a time instance at which a failure occurs.

[0062] According to an embodiment, the phase angle boundary of the fault current is determined based on the phase angle of the fault current, wherein the phase angle of the fault current depends on the fault location, wherein the fault current is a complex number, and wherein the phase angle of the fault current is the angle, phase or argument of the fault current, in particular measured during the fault.

[0063] According to an embodiment, the plurality of voltage measurements and the plurality of current measurements include or are measurements of each of a plurality of phases, in particular three phases, transmitted via the power transmission line.

[0064] According to an embodiment, Figure 5 The method illustrated in is applicable to all fault types, including in particular single-phase to ground fault, phase-to-phase fault, phase-to-phase to ground fault and three-phase to ground fault.

[0065] FIG6 illustrates a flow chart of a method according to an embodiment of the present disclosure. The flow chart of FIG6 takes into account Figure 7 , and therefore reference is made thereto. 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., power grid 721). The skilled person will appreciate that the first terminal is merely an exemplary component for illustrative purposes, and that the protected power line may be terminated by a device other than the first terminal. Similarly, the skilled person will also appreciate that the second terminal is merely an exemplary component for illustrative purposes, and that the protected power line may be terminated by a device other than the second terminal.

[0066] An electric power system may be a network of electric devices connected via transmission lines for the transmission of electric power. An electric device may be a power source, a power consumer or a power grid. A power source may be an electrical device that supplies electrical energy to an electric load, in particular by converting one form of energy into another form of energy. A power source may be a synchronous generator or an asynchronous generator (also known as an unconventional power source).

[0067] The source impedance of the second power supply 721 is modeled as a second source impedance Z connected in series to the second power supply 721. G722. The first source may be any of other unconventional power sources (i.e., unconventional power sources other than IBR), synchronous power sources, or power grids including unconventional power sources and / or synchronous power sources. Unconventional power sources may be equivalent to asynchronous power sources including IBR. The second source may be a synchronous power source or a power grid including synchronous power sources and / or unconventional power sources. According to an embodiment, the first power source is one of a power grid, a synchronous power source, an unconventional power source, and in particular an inverter-based resource, and wherein the second power source is a synchronous power source or a power grid having at least one synchronous power source and / or at least one unconventional power source. Although omitted for simplicity, the power system 700 may further include a relay 'R', which may be placed at, in, or on, or associated with, the terminal bus 'M' 710. The relay 'R' may include measuring devices, in particular current and voltage transformers (CT&PT), which measure the voltage at the bus 'M' 710 and the current passing through the bus 'M'. The voltage at the bus 'M' 710 and the current passing through the bus 'M' may also or otherwise be obtained, for example, by other measuring means. The power system 700 may further include a device, in particular an intelligent electronic device (IED), which may be placed at, 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 Figure 6. With reference to Figure 6, the first power source, the second power source and the second power source impedance are hereinafter referred to as an IBR system, a grid-side source and a grid-side source impedance.

[0068] According to an embodiment, at least one of the plurality of voltage measurements of the first terminal is measured before the fault instance and / or at least one of the plurality of voltage measurements of the first terminal is measured after the fault instance.

[0069] According to an embodiment, at least one current measurement of the plurality of current measurements of the first terminal is measured before the fault instance and / or at least one current measurement of the plurality of current measurements of the first terminal is measured after the fault instance.

[0070] The embodiment of FIG6 includes two parts: (i) pre-fault analysis 620 of grid-side source impedance, such as Figure 6b and (ii) for calculating the apparent impedance seen from the bus 'M' 710 after the correction of the post-fault analysis 630, such as Figure 6a). Data, such as voltage measurements and / or current measurements of bus 'M' 710, are acquired 610. In a pre-fault analysis 620, a grid-side equivalent source impedance 722 is evaluated and estimated based on the acquired data 612 obtained before the fault (as detected at 614). The output grid-side source impedance 628 is fed to a post-fault analysis 630 and used by it to calculate the corrected apparent impedance seen from bus 'M' 710 in the event of a fault. A detailed description of the pre-fault analysis 620 and the post-fault analysis 630 is given below.

[0071] Pre-fault analysis of grid-side source impedance 620:

[0072] At 621, an IBR event is detected based on the acquired data 612 (particularly the voltage measurement and current measurement of the first terminal) and / or based on the negative output 616 of the fault detection at 614 (i.e., when no fault is detected). An event may be any change within the IBR system 711 that causes a change in the power injected into the network from the IBR system 711. According to an embodiment, in a wind farm, an event may include a shutdown / introduction of a wind turbine unit, a change in wind speed, a cut-in / cut-out event, etc. A staged detection by intentionally modifying the inverter current reference may also be used. As a result, the current injected into the grid by the IBR via the connecting (multiple) power lines may change temporarily. Such staged events can be used to estimate grid-side equivalent parameters. At 622, a credible event may be identified based on a change in the power, voltage, and / or current bus 'M' 710 (particularly by comparing these parameters with certain threshold levels). Such changes may also be associated with event flags / signals communicated from the IBR side, particularly if there is communication between the IBR side and a connection point (e.g., bus 'M'). According to an embodiment, changes in electrical parameters of voltage, current, and / or power observed at bus 'M' 710 and concurrent changes in wind speed indicated by an anemometer reading at the park may be used as credible IBR events.

[0073] The change in the current injected from bus 'M' 710 into the protected transmission line 730 can be considered as a change in the current injected at bus 'N' 720 through the protected transmission line 730. This change in the injected current induces a voltage change at bus 'N' 720. Although the voltage measurement and current measurement of bus 'M' 710 are available, the voltage parameters and current parameters at bus 'N' 720 are not easily obtained in the absence of a dedicated communication link between bus 'M' 710 and bus 'N' 720. However, at 623, the voltage parameters and current parameters at bus 'N' 720 can be calculated based on the available voltage measurement and current measurement of bus 'M' 710 as follows:

[0074]

[0075] Among them, the matrix The model of the protected transmission line 730 is described and can be derived from the parameters of the protected transmission line 730 (particularly the resistance, inductance and capacitance per unit length). The symbol Δ represents the change relative to the steady-state value (i.e., the value of the entity before the IBR event occurs). In the case of a single event, the grid-side source impedance 722 can be calculated at 624 as follows:

[0076]

[0077] Due to the random nature of system load, grid-side parameters, especially the equivalent source voltage of IBR (i.e., Figure 1 E M ∠δ) may be a continuously changing parameter, i.e., the load in the power system changes continuously and therefore the source equivalent of the power grid also changes continuously. The source equivalent may be estimated based on an overdetermined set of equations generated by a plurality of events. Therefore, the source impedance calculation may be expressed as a least squares approximation. Relative to the calculation at 624, the least squares estimate at 624 in the case of a plurality of events may more accurately estimate the grid side source impedance 722 under noisy actual conditions. The least squares expression based on p events may be expressed as follows:

[0078]

[0079] Where p is a natural number greater than 1, and where A is defined for the i-th event as follows i and b i :

[0080]

[0081] Both the calculation and estimation procedures described above can be implemented on a data window after an IBR event. For example, a data window of 0.2 seconds in length after an IBR event can be selected. An estimation of the grid-side source impedance 722 can be implemented for each data point in the window. The final estimate for the data window can be obtained as the average of the estimates obtained for each data point. In doing so, the grid-side source impedance estimate 628 is obtained based on (particularly only based on) the measured values ​​that can be obtained at bus 'M' 710, and can be included in the process for accurately calculating the corrected apparent impedance seen from bus 'M' 710, especially for the transmission line connected to the IBR system 711.

[0082] Post-failure analysis 630 (scope elements):

[0083] The post-fault analysis 630 obtains the measurements (particularly the voltage and current measurements) of the bus 'M' 710 obtained before and after the fault occurrence instance and the estimated value of the grid-side source impedance 628. After the fault detection at 614, the measured apparent impedance Z is calculated at 631 according to equation (8) R . It should be noted that the term "fault detection" in distance relaying may imply the identification of a fault event from normal load conditions based on voltage measurements and / or current measurements. Range may be the apparent impedance measured at a measurement location on the transmission line or, in the event of a fault, within the terminals terminating the transmission line (particularly through a relay). Underrange may be a situation that occurs when the relay measures an impedance greater than the actual value (particularly the apparent impedance as seen from the relay), which may result in the relay not operating for an in-zone fault. Overrange may be a situation that occurs when the relay measures an impedance less than the actual value (particularly the apparent impedance as seen from the relay), which may result in the relay operating for an out-of-zone fault.

[0084]

[0085] The measured apparent impedance may deviate from the actual apparent impedance seen from the observation point due to a fault, especially when there are no other effects affecting the apparent impedance. The main challenge is to obtain an apparent impedance that is corrected to achieve the remote feed-in effect, since the corrected apparent impedance should be a better measure of the impedance of the faulted line section. The corrected apparent impedance may be determined as follows

[0086]

[0087] Among them, φ R and φ 1L They represent the apparent impedance Z R The phase angle of the fault current I F Angle. Fault current I F However, the fault current can be measured from the incremental relay current ΔI R To express it as follows:

[0088] I F =ΔI R ×CDF (10)

[0089] Where CDF represents the current distribution factor given by:

[0090]

[0091] Among them, ΔI Rrepresents the difference between the current measured by relay 'R' before and after the fault, Z L represents the impedance of the protected transmission line 730, Z G represents the grid-side source impedance, and Z IBR Represents the modeled source impedance of the IBR system connected in series to the modeled voltage source of the IBR system.

[0092] Therefore, according to equation (10), the fault current I can be expressed as follows F Angle:

[0093] ∠I F =∠ΔI R +∠CDF (12)

[0094] Since the relay current I R is the measured quantity, so the incremental relay current ΔI can be obtained R , and the phase angle of the CDF can be calculated. Z can be calculated dynamically after the fault at 632 as follows IBR :

[0095]

[0096] where Δ represents the change from the value before the fault. L can be obtained as input and Z G is estimated at 620, therefore, the numerator of equation (11) and its phase angle can be dynamically calculated during a fault. However, the denominator term (1-d)Z of equation (11) L +Z G is still unknown, since the location of the fault "d" is not known a priori. Figure 8 , which illustrates a graphical representation of the apparent impedance range calculated according to an embodiment of the present disclosure, it can be inferred that for a fault on the protected transmission line 730, the phase angle of the denominator term of equation (11) can only be within the feasible range. For a fault toward the remote end of the line (i.e., d=1), the phase angle is determined by the grid-side source impedance Z G For a close-in fault (i.e., d=0), the phase angle is determined by the grid-side source impedance Z G 720 and the line impedance Z of the protected transmission line 730 L Based on the above-described reasoning, the corrected apparent impedance is calculated as described in detail below.

[0097] The two CDFs may be calculated at 633 as follows:

[0098]

[0099] For each CDF above, the two angles of the fault current are obtained as follows:

[0100] ∠IF1=∠ΔI R +LCDF1 (16)

[0101] ∠IF2=∠ΔI R +∠CDF2 (17)

[0102] The CDFs of Equations (14) and (15) may be calculated based on a unit distance d that satisfies 0≤d≤1.

[0103] According to an embodiment, for a fault occurring in a section of the power transmission line between the first terminal and the second terminal, the phase angle boundary is or comprises a minimum phase angle and a maximum phase angle of the fault current.

[0104] According to an 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 wherein 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, the second position being different from the first position.

[0105] According to an embodiment, the first phase angle is a minimum phase angle of the fault current and wherein the second phase angle is a maximum phase angle of the fault current.

[0106] The fault current angle ∠I thus obtained is used F1 and ∠I F2 , the two corrected apparent impedances are calculated at 634 by substituting the parameters into equation (9) as follows and

[0107]

[0108] Since for a fault on the protected transmission line 730, the denominator term (1-d)Z of equation (11) L +Z G can only be located within the feasible region (including the boundary of the region), such as Figure 8 As shown in , the final solution of the corrected apparent impedance can only be located at and The final solution can be determined as follows and The weighted average of:

[0109]

[0110] Among them, W d and W s They are and Scaling factor W d and W s The sum satisfies W d +W s =1. If W d >W s , then a reliable solution is obtained at 635 And if W s >W d , then a safe solution is obtained at 635 The solution can be used together at 636 and To obtain a deterministic solution. and Both indicate that the fault is located in the front half of the protected transmission line 730, then If they together indicate that the fault is in the second half of the protected transmission line 730, then If neither of these two conditions is met, the final solution can be considered and The above statement is summarized as follows:

[0111]

[0112] The calculated final corrected apparent impedance can be fed to devices, controllers and computer readable media, relays, relay decision logic, etc. for further processing and / or determining fault location and / or controlling protection systems for the power system.

[0113] According to an embodiment, and are the first apparent impedance and the second apparent impedance respectively.

[0114] According to an embodiment, the method further comprises determining a source impedance of the second power source based on the plurality of voltage measurements and the plurality of current measurements of 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.

[0115] According to an embodiment, the source impedance of the second power source is determined based on the plurality of voltage measurements and the plurality of current measurements obtained prior to the fault instance.

[0116] According to an embodiment, the method further comprises 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 obtained 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.

[0117] According to an embodiment, and are the third apparent impedance and the fourth apparent impedance respectively.

[0118] According to an 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 summing, more particularly, summing using a first weight for scaling the first apparent impedance and a second weight for scaling the second apparent impedance, wherein the first weight is different from the second weight.

[0119] According to an embodiment, is the fifth apparent impedance.

[0120] According to an embodiment, the method further comprises 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 the line impedance of the transmission line and a second ratio of the fourth apparent impedance to the line impedance of the transmission line, wherein the protection system is controlled based on the fifth apparent impedance.

[0121] The embodiments described above are based on an exemplary power system under test (such as Fig. 9) is illustrated. The power system is modeled with power system computer-aided design (PSCAD). The power system 900 includes a protected power line 930, which is terminated by a first terminal (i.e., bus 'M' 910) connected to a first power source (i.e., IBR system 911) and by a second terminal (i.e., bus 'N' 920) connected to a second power source 921. In addition to bus 'N' 920, the rest of the second power source 921 can be modeled as a Thevenin equivalent (an equivalent combination of constant voltage sources connected in series to a source impedance). The first source can be any of other unconventional power sources (i.e., unconventional power sources other than IBR), synchronous power sources, or power grids including unconventional power sources and / or synchronous power sources. The second source can be a synchronous power source or a power grid including synchronous power sources and / or unconventional power sources. Although omitted for simplicity, the power system 900 may further include a relay 'R', which may be placed at, in, or on, or associated with, the terminal bus 'M' 910. Relay 'R' may include measuring devices, in particular current and voltage transformers (CT&PT), which measure the voltage at bus 'M' 910 and the current passing through the bus 'M'. The voltage at bus 'M' 910 and the current passing through the bus 'M' may also or otherwise be obtained, for example by other measurement means. The power system 900 includes devices, in particular intelligent electronic devices (IEDs), each of which is placed at, in or on bus 'M' 910 or associated with bus 'M' 910. It should be noted that the measurements obtained at bus 'N' 920 and through bus 'N' provide reference values ​​(data points marked as 'actual' in Figures 10 to 11) and are not used to calculate the final corrected apparent impedance according to any of the embodiments described above. 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 FIG6. Fig. 9 , the source impedance of the second power supply 921 is called the grid-side source impedance.

[0122] Pre-fault analysis (grid side source impedance estimation):

[0123] For illustration purposes, the grid side source impedance is maintained at 15∠84° ohms. The following are illustrated: (i) using ideal measurements to calculate the grid side source impedance during the IBR event in the case of a single IBR event, as calculated at 624; and (ii) using noisy measurements to estimate the grid side source impedance in the case of multiple IBR events, as calculated at 625. To trigger the calculation / estimation procedure, the percentage thresholds of the measured parameter change of bus 'M' 910 are considered to be: 0.2% for voltage, 5% for current and 5% for power. FIG. 10 illustrates the following in the case of multiple IBR events: Fig. 9 The measured values ​​and grid-side source impedance at bus 'M' 910 during a single event in the unconventional power supply disclosed in . In particular, Fig.10a ), b) and c) illustrate the percentage of voltage, current and power measured at the POC bus 'M' 910 during a wind speed change event occurring at the IBR system 911. Fig.10d )and Fig.10e ) illustrates the magnitude and angle of the grid-side source impedance. These estimates are calculated according to equations (4)-(5). The average magnitude of the estimated grid-side source impedance is approximately 14.76Ω (error 1.6%), and the average phase angle of the estimated grid-side source impedance is approximately 83.8° (error 0.2%).

[0124] Figure 11 shows the measurement results under noisy conditions. Fig. 9 The source impedance of the remote power supply during multiple events in the unconventional power supply disclosed in . In particular, Fig.11a )and Fig.11b ) illustrates the magnitude and angle of the grid-side source impedance in the case of a single IBR event. These estimates are calculated according to equations (4)-(5). The average magnitude of the estimated grid source impedance is approximately 13.68Ω (error 8.8%), and the average phase angle of the estimated grid source impedance is approximately 89.56° (error 6.6%). Fig.11c )and Fig.11d ) illustrates the magnitude and angle of the grid-side source impedance from three IBR events. These estimates are calculated using a least squares estimation procedure based on 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 14.86Ω (error 0.9%), and the average phase angle of the estimated grid-side source impedance is approximately 84.64° (error 0.8%). Thus, an overall improvement in estimation accuracy is observed.

[0125] Post-fault analysis (calculation of apparent impedance after final correction):

[0126] A distance relay (IED) at bus 'M' 910 and two fault scenarios are considered. In scenario 1, the grid side source impedance is considered to be homogeneous with respect to the line impedance and is maintained at 15∠84° ohms. A fault at a distance of 90km from bus 'M' is simulated. In scenario 2, the grid side source impedance is considered to be inhomogeneous and is maintained at 15∠65° ohms. A fault at a length of 75km from bus 'M' is simulated. In each of these cases, the fault is considered to be an arcing with a resistance of 10 ohms. It is expected that the relay at bus 'M' should not detect the fault of scenario 1 in its zone-1, while the relay should detect the fault of scenario 2 in zone-1.

[0127] Scenario-1:

[0128] Fig.12 A summary of numerical results of apparent impedance calculated according to various methods (including a method according to an embodiment of the present disclosure) for Scenario-1 is illustrated. Fig.13 FIG. 4 illustrates a graphical representation of the apparent impedance calculated according to various methods (including the method according to an embodiment of the present disclosure) for scenario-1. Fig.12 and Fig.13 , the measured apparent impedance 1220 falls outside zone-1. However, the value of the apparent impedance is much higher than the faulty line section impedance dZ l 1210. For this fault, the compensated apparent impedance 1230 is invalid and out of range (i.e., the fault is identified as Zone-1 when it is not actually such). The compensated apparent impedance 1230 is calculated by simplifying the assumptions about the grid side source impedance relative to the IBR side source impedance. The apparent impedance calculated according to an embodiment of the present disclosure 1240 indicates that the fault is located in the second half of the line and therefore the final solution is taken according to equation (21) as It is located outside of zone-1. Therefore, the method according to the embodiment of the present disclosure correctly identifies the fault as being outside zone-1 of the relay. Fig.13 , the final apparent impedance calculated according to an embodiment of the present invention is Closely locate the faulty line section impedance dZ l 1210, which indicates its higher accuracy in locating faults.

[0129] Scenario-2:

[0130] Fig.14 A summary of numerical results of apparent impedance calculated according to various methods, including a method according to an embodiment of the present disclosure, is illustrated. Fig.15 Graphs showing apparent impedance calculated according to various methods, including methods according to embodiments of the present disclosure, are illustrated. Fig.14 and Fig.15 , the measured apparent impedance 1420 calculation failed to detect the fault in relay zone-1. The corrected apparent impedance calculated according to the embodiment of the present disclosure 1440 (calculated by the proposed method) indicates that the fault is located in the second half of the line and therefore the final solution according to equation (21) is taken as It is located inside zone-1. Therefore, the method according to the embodiment of the present disclosure correctly identifies the fault as being within zone-1 of the relay. Fig.13 , the final apparent impedance value calculated according to an embodiment of the present invention is The faulted line section impedance is closely localized, indicating a higher accuracy in locating the fault. In contrast, for this fault, the compensated apparent impedance 1430 is inaccurate and under-ranged (ie, fails to identify the fault as such when it is actually a fault in Zone-1).

[0131] FIG. 16 illustrates an apparatus, a computer-readable medium, and a power system according to an embodiment of the present disclosure.

[0132] Device 1610 is a device for controlling a protection system for an electric power system, the electric power system comprising a transmission line terminated with a first terminal connected to a first power source and a second terminal connected to a second power source, the device comprising a processor configured to: obtain a plurality of voltage measurements and a plurality of current measurements of the first terminal; determine phase angle boundaries of a fault current based on the plurality of voltage measurements and the plurality of current measurements; determine a first apparent impedance starting from the first terminal based on a first phase angle within or at one of the phase angle boundaries; determine a second apparent impedance starting from the first terminal based on a second phase angle within or at one of the phase angle boundaries; determine a third apparent impedance and a fourth apparent impedance starting 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.

[0133] According to an embodiment, the processor is further configured to perform the method of any one of the embodiments described above.

[0134] The computer readable medium 1620 is a device for controlling a protection system for a power system, which carries instructions for executing the method of any one of the embodiments described above.

[0135] The power system 1600 includes a power transmission line 1630 , an apparatus 1610 of any one of the embodiments described above, and a computer-readable medium 1620 of any one of the embodiments described above.

[0136] Although various embodiments of the present disclosure have been described above, it should be understood that they are presented only as examples and not as limitations. Similarly, various figures may depict example architectures or configurations, which are provided to enable those of ordinary skill in the art to understand the exemplary features and functions of the present disclosure. However, such personnel will understand that the present disclosure is not limited to the illustrated example architectures or configurations, but can be implemented using various alternative architectures and configurations. Additionally, as will be understood by those of ordinary skill in the art, one or more features of an embodiment may be combined with one or more features of another embodiment described herein. Therefore, the breadth and scope of the present disclosure should not be limited by any of the exemplary embodiments described above.

[0137] It should also be understood that any reference to an element herein using names such as "first," "second," etc. does not generally limit the number or order of those elements. Rather, these names 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 element and a second element does not mean that only two elements may be employed, or that the first element must be located before the second element in some manner.

[0138] Additionally, those of ordinary skill in the art will appreciate that information and signals may be represented using any of a variety of different techniques and technologies. For example, data, instructions, commands, information, signals, bits, and symbols such as those referenced in the above description may be represented by voltage, current, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

[0139] The skilled person will further understand that any of the various illustrative logical blocks, units, processors, devices, circuits, methods, and functions described in conjunction with the aspects disclosed herein may be implemented by electronic hardware (e.g., digital implementations, analog implementations, or a combination of both), firmware, various forms of programs or design codes combined with instructions (which for convenience may be referred to herein as "software" or "software units"), or any combination of these technologies.

[0140] In order to clearly illustrate this interchangeability of hardware, firmware and software, various illustrative components, blocks, units, circuits and steps have been generally described above with respect to their functions. Whether such functions are implemented as hardware, firmware or software or a combination of these technologies depends on specific applications and the design constraints imposed on the entire system. Technicians can implement the described functions in various ways for each specific application, but such implementation decisions will not cause deviations from the scope of the present disclosure. According to various embodiments, processors, devices, components, circuits, structures, machines, units, etc. can be configured to perform one or more of the functions described herein. As used herein with respect to a specified operation or function, the term "configured to" or "configured to be used for" refers 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.

[0141] In addition, the skilled person will understand that the various illustrative methods, logic blocks, units, devices, components and circuits described herein may 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 logic blocks, units and circuits may further include antennas and / or transceivers to communicate with various components within a network or within a device. The general-purpose processor may be a microprocessor, but in an alternative, the processor may be any conventional processor, controller or state machine. The processor may also be implemented as a combination of computing devices, for example, a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors combined with a DSP core, or any other suitable configuration to perform the functions described herein. If implemented in software, the functions may be stored on a computer-readable medium as one or more instructions or codes. Therefore, the steps of the methods or algorithms disclosed herein may be implemented as software stored on a computer-readable medium.

[0142] Computer-readable media include both computer storage media and communication media, including any media that can be enabled to transfer a computer program or code from one place to another. Storage media can be any available media that a computer can access. As an example and not limitation, such computer-readable media can include RAM, ROM, EEPROM, CD-ROM or other optical disk storage devices, magnetic disk storage devices or other magnetic storage devices, or any other media that can be used to store desired program code in the form of instructions or data structures and can be accessed by a computer.

[0143] Additionally, memory or other storage devices and communication components may be used in embodiments of the present disclosure. It will be appreciated that, for purposes of 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 functions between different functional units, processing logic elements, or domains may be used without devaluing the present disclosure. For example, functions illustrated as being performed by separate processing logic elements or controllers may be performed by the same processing logic element or controller. Therefore, references to specific functional units are only references to appropriate means for providing the described functions, rather than indicating a strict logical or physical structure or organization.

[0144] Various modifications to the embodiments 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 embodiments without departing from the scope of this disclosure. Therefore, this disclosure is not intended to be limited to the embodiments shown herein, but is to be given the widest scope consistent with the novel features and principles disclosed herein, as recited in the appended claims.

Claims

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

2. The method according to claim 1, wherein: For a fault occurring in a section of the transmission line between the first terminal and the second terminal, the phase angle boundary is or includes a minimum phase angle and a maximum phase angle of the fault current.

3. The method according to claim 1 or 2, 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 wherein 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 that is different from the first position.

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

5. The method according to any one of claims 1 to 4, comprising: A source impedance of the second power source is determined based on the plurality of voltage measurements and the plurality of current measurements of 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.

6. The method according to 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 obtained prior to a fault instance.

7. The method according to any one of claims 1 to 6, wherein: The first power source is one of a grid, a synchronous power source, an unconventional power source, in particular an inverter-based resource, and wherein the second power source is a synchronous power source or a grid having at least one synchronous power source and / or at least one unconventional power source.

8. The method according to any one of claims 1 to 7, comprising: An impedance of the first power source after the fault instance is determined based on the plurality of voltage measurements and the plurality of current measurements obtained 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. The method according to any one of claims 1 to 8, wherein: 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 summing, more particularly, summing using a first weight for scaling the first apparent impedance and a second weight for scaling the second apparent impedance, wherein the first weight is different from the second weight.

10. The method according to any one of claims 1 to 9, comprising: A fifth apparent impedance is determined 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, wherein the protection system is controlled based on the fifth apparent impedance.

11. The method according to any one of claims 1 to 10, wherein: At least one of the plurality of voltage measurements of the first terminal is measured before a fault instance and / or at least one of the plurality of voltage measurements of the first terminal is measured after the fault instance.

12. The method according to any one of claims 1 to 11, wherein: At least one current measurement of the plurality of current measurements of the first terminal is measured before a fault instance and / or at least one current measurement of the plurality of current measurements of the first terminal is measured after the fault instance.

13. An apparatus for controlling a protection system for an electric power system, the electric power system comprising a transmission line, the transmission line being terminated by a first terminal coupled to a first power source and a second terminal coupled to a second power source, the apparatus comprising a processor, the processor being configured to: obtaining a plurality of voltage measurements and a plurality of current measurements of 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 from the first terminal based on a first phase angle within or at one of the phase angle boundaries; determining a second apparent impedance from the first terminal based on a second phase angle within or at one of the phase angle boundaries; determining a third apparent impedance and a fourth apparent impedance starting from the first terminal based on the first apparent impedance and the second apparent impedance; as well as The protection system is controlled based on the third apparent impedance and the fourth apparent impedance.

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

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

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