Parameter estimation for multi-terminal lines.

Abstract

The present disclosure relates to a method for determining at least one network parameter of a network including a power line terminated by at least three terminals, the method including: obtaining measurements of at least three terminals terminating the power line at each end of the power line; obtaining at least one input parameter for a network model of the network based on the obtained measurements of the at least three terminals; determining the at least one network parameter based on the at least one input parameter for the network model and the network model; and providing the at least one network parameter to an apparatus configured to control, monitor, and / or analyze the network. The present disclosure also relates to respective apparatus and systems.

Description

[Technical Field]

[0001] Technical Field The present disclosure relates to a method, apparatus, computer-readable medium, and system for determining at least one network parameter of a network comprising a power line terminated by at least three terminals. [Background technology]

[0002] background In power system protection, fault location, and control, parameters, especially transmission line parameters, are often assumed to be known but may contain errors that can affect resulting performance. Therefore, parameter estimation and verification are increasingly important areas for power systems. Transmission line parameters can depend on ambient system conditions, including temperature, line aging, and so on. Therefore, online estimation of line parameters is highly desirable to obtain accurate line parameters, which is particularly beneficial for fault location and protection applications. Parameter estimation for lines connected to renewable resources is particularly challenging and crucial for adaptive protection applications.

[0003] The first approach estimates line parameters of a three-terminal mixed line using positive and negative phase, pre-fault and during-fault voltages and currents, and may further identify the fault section and fault location, but is limited to cases where the transmission line is only coupled to conventional sources such as synchronous sources. For scenarios where negative-sequence quantities are not available, especially networks connected to inverter-based resources (IBRs), the first approach may require multiple sets of pre-fault measurements depending on the IBR type and control to resolve the line parameters.

[0004] A second approach may estimate line parameters of a three-terminal transmission line using nonlinear weighted least-square error (NWLSE) from phasor measurement unit (PMU) and supervisory control and data acquisition (SCADA) measurements. This approach may require at least three distinct measurement sets to estimate the line parameters. Recording multiple data sets requires large amounts of storage and is computationally intensive for the IED.

[0005] The third approach may utilize analytical optimization techniques such as Newton's method and least-squares methods, but the convergence of these methods is highly dependent on initial guesses. This approach may use a metaheuristic algorithm to solve a nonlinear objective function in step 1, and in step 2, the results of step 1 are provided as initial guesses to the Newton-Raphson algorithm to estimate the line parameters of the two-terminal mixed line. Metaheuristic optimization methods do not guarantee a global optimum and may result in local minima, making them difficult to implement on IED platforms.

[0006] The above-described techniques may have limitations when the transmission line is connected to an IBR and the initial guess is insufficient. Therefore, there is a need for improved methods, apparatus, computer-readable media, and systems for determining at least one network parameter of a network comprising a power line terminated by at least three terminals. Summary of the Invention [Means for solving the problem]

[0007] overview In particular, it would be advantageous to achieve parameter estimation for networks with at least one inverter-tied source connected to at least one terminal of a transmission line. In doing so, it is desirable to implement a single-stage or two-stage method for solving line parameters for a three-terminal uniform or mixed line by eliminating the risk of poor initial guesses based on only one set of measurement data (pre-fault).

[0008] The present disclosure relates to a method for determining at least one network parameter of a network comprising a power line terminated by at least three terminals, the method including: obtaining measurements, particularly measurements taken before a fault, of at least three terminals terminating the power line at each end of the power line, the power line comprising respective sections that are portions of the power line from a location on the power line to each end, and at least one electrical parameter of each section being different from the electrical parameters of the other respective sections; obtaining at least one input parameter for a network model of the network based on the obtained measurements of the at least three terminals, the at least one input parameter for the network model being an electrical parameter of the network model, particularly an impedance of one of the respective sections of the power line; determining the at least one network parameter based on the at least one input parameter for the network model and the network model; and providing the at least one network parameter to a device configured to control, monitor, and / or analyze the network.

[0009] The present disclosure also relates to a method for determining at least one network parameter of a network comprising a power line terminated by at least three terminals, the method including: obtaining measurements of at least three terminals terminating the power line at respective ends of the power line, the power line comprising respective sections that are portions of the power line from a location on the power line to the respective ends, the measurements being taken before a fault, and wherein at least one electrical parameter of the respective sections is different from an electrical parameter of the other respective sections; obtaining at least one input parameter for a network model of the network based on the obtained measurements of the at least three terminals, the at least one input parameter for the network model being an electrical parameter of the network model, in particular an impedance of one of the respective sections of the power line; determining the at least one network parameter based on the at least one input parameter for the network model and the network model; and providing the at least one network parameter to a device configured to control, monitor, and / or analyze the network.

[0010] It will be understood by those skilled in the art that pre-fault measurements may refer to measurements taken in the absence of a fault, i.e., in the absence of a fault.

[0011] The network may be a power transmission network. A power line may be a cable or other structure that carries electrical energy in an electrical power system / network, especially by conducting electromagnetic waves. A power line may also be a transmission line.

[0012] A terminal may refer to the point where a conductor, particularly a transmission line or network, terminates. A terminal may also refer to an electrical connector at this end, acting as an interface to further conductors and creating a point to which an external circuit can be connected. A terminal may also be an electrical bus, particularly a busbar and / or bus duct, used to connect high-voltage equipment.

[0013] The network parameter may be one or more line parameters, such as resistance, inductance, and / or capacitance.

[0014] The electrical parameters of a section may refer to the impedance of the section, particularly the modeled impedance. The electrical parameters of a section may refer to the positive, negative, or zero-phase series impedance of the section, particularly the positive, negative, or zero-phase series impedance including the positive, negative, or zero-phase resistance of the section and / or the positive, negative, or zero-phase inductance of the section. The electrical parameters of a section may refer to the shunt admittance of the section, particularly the modeled shunt admittance. The electrical parameters of a section may refer to the positive, negative, or zero-phase shunt admittance of the section, particularly the positive, negative, or zero-phase shunt admittance including the positive, negative, or zero-phase susceptance of the section.

[0015] The electrical parameters of a section may refer to the voltage and / or current and / or propagation constant of the section. The electrical parameters of a section may particularly refer to the values ​​of the electrical parameters, for example the voltage value and / or current value and / or propagation constant of the section.

[0016] The propagation constant may be expressed as γ=α+jβ, where α is the attenuation constant and β is the phase constant.

[0017] The input parameters for the network model are the electrical parameters of the network model, for example, the impedance and / or inductance of the network model.

[0018] A terminal may be an electrical connector that terminates a first electrical cable and connects to a second electrical cable, thereby transmitting current between them. A transmission line may be an overhead wire or cable, especially an underground cable. Each section of a transmission line may be the same or different, and may be an overhead wire or cable.

[0019] The network model may be a distributed model or a series impedance model, as will be further exemplarily explained below. The line capacitance of a section may be the capacitance between a section of a transmission line and another object, in particular a conductive material, for example another section of the transmission line. The line capacitance of a section may be the capacitance between two phases or between lines of the same section of the transmission line. The line capacitance of a section may couple the section of the transmission line to electrical ground potential.

[0020] A fault may refer to a fault condition in a transmission line or a section of a transmission line. A fault location is the location on the transmission line where the fault occurs. A fault may refer to any form of anomaly in a system, i.e., any operating condition that differs from the normal operating condition of the system.

[0021] According to one embodiment, obtaining at least one input parameter for the network model includes or is determining at least one input parameter for the network model based on the obtained measurements of the at least three terminals and the further network model.

[0022] According to one embodiment, the further network model differs from the network model used to determine the at least one network parameter in that the network model includes at least one more electrical parameter than the further network model, in particular a propagation constant of one of the respective sections of the power line or a line capacitance of one of the respective sections of the power line coupling one of the respective sections to an electrical ground potential.

[0023] According to one embodiment, at least one input parameter for the network model is determined adaptively to differences in electrical parameters between respective sections of the power line modeled in the further network model.

[0024] According to one embodiment, the at least one network parameter is determined adaptively to differences in electrical parameters between respective sections of the power line modeled in the further network model.

[0025] According to one embodiment, the method further includes determining the failed section based on at least one input parameter for the network model.

[0026] According to one embodiment, the method further comprises controlling an electric power device, in particular an auto-recloser for the electric power line, based on the determined faulted section.

[0027] According to one embodiment, the method further includes estimating a fault location based on the determined faulted section, at least one electrical parameter of the network model, and voltage and current fault phasors measured during the fault, particularly when the power device operates in the first operating mode in response to the control.

[0028] According to one embodiment, the method further includes providing the at least one network parameter to a device configured to control, monitor, and / or analyze the network.

[0029] The present disclosure also relates to an apparatus for determining at least one network parameter of a network comprising a power line terminated by at least three terminals, the apparatus comprising a processor configured to: acquire measurements of at least three terminals terminating the power line at respective ends of the power line, the power line comprising respective sections that are portions of the power line from a location on the power line to the respective ends, wherein at least one electrical parameter of each section differs from an electrical parameter of each of the other sections; acquire at least one input parameter for a network model of the network based on the acquired measurements of the at least three terminals, the at least one input parameter for the network model being an electrical parameter of the network model, in particular an impedance of one of the respective sections of the power line; determine the at least one network parameter based on the at least one input parameter for the network model and the network model; and provide the at least one network parameter to an apparatus configured to control, monitor, and / or analyze the network.

[0030] The present disclosure also relates to an apparatus for determining at least one network parameter of a network comprising a power line terminated by at least three terminals, the apparatus comprising a processor configured to: obtain measurements of at least three terminals terminating the power line at respective ends of the power line, the power line comprising respective sections that are portions of the power line from a location on the power line to the respective ends, the measurements being taken before a fault, and wherein at least one electrical parameter of the respective sections is different from an electrical parameter of the other respective sections; obtain at least one input parameter for a network model of the network based on the obtained measurements of the at least three terminals, the at least one input parameter for the network model being an electrical parameter of the network model, in particular an impedance of one of the respective sections of the power line; determine the at least one network parameter based on the at least one input parameter for the network model and the network model; and provide the at least one network parameter to an apparatus configured to control, monitor, and / or analyze the network.

[0031] It will be understood by those skilled in the art that measurements prior to a fault may also refer to measurements taken in the absence of a fault, i.e., in the absence of a fault.

[0032] According to one embodiment, the processor is configured to obtain at least one input parameter for the network model by determining at least one input parameter for the network model based on the obtained measurements of the at least three terminals and the further network model.

[0033] According to one embodiment, the further network model is different from the network model used to determine the at least one network parameter.

[0034] According to one embodiment, the network model includes at least one more electrical parameter than the further network model, in particular a propagation constant of one of the respective sections of the power line or a line capacitance of one of the respective sections of the power line coupling one of the respective sections to electrical ground potential.

[0035] According to one embodiment, the processor is configured to determine at least one input parameter for the network model in accordance with a difference in an electrical parameter between respective sections of the power line modeled in the further network model.

[0036] According to one embodiment, the processor is configured to determine the at least one network parameter adaptively to differences in electrical parameters between respective sections of the power line modeled in the further network model.

[0037] According to one embodiment, the processor is further configured to determine the failed section based on at least one input parameter for the network model.

[0038] According to one embodiment, the processor is further configured to control an electric power device, in particular an auto-recloser for the electric power line, based on the determined faulted section.

[0039] According to one embodiment, the processor is further configured to estimate a fault location based on the determined faulted section, at least one electrical parameter of the network model, and voltage and current fault phasors measured during the fault, particularly when the power device operates in the first operating mode in response to the control.

[0040] According to one embodiment, the processor is further configured to provide the at least one network parameter to a device configured to control, monitor, and / or analyze the network.

[0041] 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 determining at least one network parameter of a network comprising a power line terminated by at least three terminals.

[0042] According to one embodiment, an apparatus configured to control, monitor, and / or analyze a network is or includes a computer-readable medium according to the above-described embodiments.

[0043] The present disclosure further relates to a system comprising a network comprising a power line terminated by at least three terminals and an apparatus according to any of the above embodiments.

[0044] According to one embodiment, the system further comprises an auto-reclosing device for the power equipment, in particular the power lines.

[0045] The following aspects refer to specific embodiments of the invention. 1. A method for determining at least one network parameter of a network comprising a power line terminated by at least three terminals, comprising: obtaining measurements of at least three terminals terminating the power line at each end of the power line, in particular measurements taken before the fault, the power line comprising respective sections being portions of the power line from a location on the power line to each of the ends; obtaining an electrical parameter of at least one of the respective sections that is different from an electrical parameter of each of the other respective sections; obtaining at least one input parameter for a network model of the network based on the obtained measurements of the at least three terminals; obtaining at least one input parameter for the network model, the input parameter being an electrical parameter of the network model, in particular the impedance of one of the respective sections of the power line; determining at least one network parameter based on the at least one input parameter for the network model and the network model; providing at least one network parameter to a device configured to control, monitor, and / or analyze the network; A method comprising:

[0046] 2. Obtaining at least one input parameter for the network model includes or is determining at least one input parameter for the network model based on the obtained measurements of the at least three terminals and the further network model; The additional network model is different from the network model used to determine the at least one network parameter; The method of embodiment 1, wherein the network model includes at least one more electrical parameter than the further network model, in particular a propagation constant of one of the respective sections of the power line or a line capacitance of one of the respective sections of the power line coupling one of the respective sections to an electrical ground potential.

[0047] 3. The method of aspect 2, wherein at least one input parameter for the network model is determined adaptively to differences in electrical parameters between respective sections of the power line modeled in the further network model, and / or at least one network parameter is determined adaptively to differences in electrical parameters between respective sections of the power line modeled in the further network model.

[0048] 4. Determining a faulted section based on at least one input parameter for the network model; Controlling an automatic reclosing device for a power device, particularly a power line, based on the determined faulty section; The method of any one of aspects 1 to 3, further comprising:

[0049] 5. Estimating a fault location based on the determined faulted section, at least one electrical parameter of the network model, and voltage and current fault phasors measured during the fault, particularly when the power device operates in a first operating mode in response to the control; providing at least one network parameter to a device configured to control, monitor, and / or analyze the network; 5. The method of embodiment 4, further comprising:

[0050] 6. An apparatus for determining at least one network parameter of a network comprising a power line terminated by at least three terminals, the apparatus comprising: a processor; obtaining measurements of at least three terminals terminating the power line at respective ends of the power line, the power line comprising respective sections that are portions of the power line from a location on the power line to the respective ends; obtaining an electrical parameter of at least one of the respective sections that is different from an electrical parameter of each of the other respective sections; obtaining at least one input parameter for a network model of the network based on the obtained measurements of the at least three terminals; obtaining at least one input parameter for the network model, the input parameter being an electrical parameter of the network model, in particular the impedance of one of the respective sections of the power line; determining at least one network parameter based on the at least one input parameter for the network model and the network model; providing at least one network parameter to a device configured to control, monitor, and / or analyze the network; 11. An apparatus comprising: a processor configured to:

[0051] 7. The processor is configured to obtain at least one input parameter for the network model by determining at least one input parameter for the network model based on the obtained measurements of the at least three terminals and the further network model; The additional network model is different from the network model used to determine the at least one network parameter; The apparatus of embodiment 6, wherein the network model includes at least one more electrical parameter than the further network model, in particular a propagation constant of one of the respective sections of the power line or a line capacitance of one of the respective sections of the power line coupling one of the respective sections to an electrical ground potential.

[0052] 8. The apparatus of aspect 7, wherein the processor is configured to determine at least one input parameter for the network model adaptively to differences in electrical parameters between respective sections of the power line modeled with the further network model, and / or the processor is configured to determine at least one network parameter adaptively to differences in electrical parameters between respective sections of the power line modeled with the further network model.

[0053] 9. The processor determining a faulty section based on at least one input parameter for the network model; Controlling an automatic reclosing device for a power device, particularly a power line, based on the determined faulty section; The apparatus of any one of aspects 6 to 8, further configured to:

[0054] 10. The processor estimating a fault location based on the determined faulted section, at least one electrical parameter of the network model, and voltage and current fault phasors measured during the fault, particularly when the power device operates in a first operating mode in response to the control; providing at least one network parameter to a device configured to control, monitor, and / or analyze the network; 10. The apparatus of embodiment 9, further configured to:

[0055] 11. A computer-readable medium carrying instructions for performing a method according to any one of aspects 1 to 5 for determining at least one network parameter of a network comprising a power line terminated by at least three terminals.

[0056] 12. A system comprising: a network comprising a power line terminated by at least three terminals; and the device according to any one of aspects 6 to 10.

[0057] 13. The system of aspect 12, further comprising an automatic reclosing device for a power device, particularly a power line.

[0058] 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 apparatuses 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 may be made while remaining within the scope of the present disclosure.

[0059] 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 example 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.

[0060] 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.

[0061] These and other aspects and implementations thereof are described in more detail in the drawings, description, and claims.

[0062] BRIEF DESCRIPTION OF THE DRAWINGS [Brief explanation of the drawings]

[0063] [Figure 1a)] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 1b] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 2] 1 shows a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 3] FIG. 1 illustrates a series impedance (RL) model of a three-terminal network according to an embodiment of the present disclosure. [Figure 4] FIG. 1 illustrates a distributed (RLC) model of a three-terminal network according to an embodiment of the present disclosure. [Figure 5] 1 shows a flowchart of a method according to one embodiment of the present disclosure. [Figure 6] 1 shows a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 7] 1 illustrates a graphical simulation result of a three-terminal network according to one embodiment of the present disclosure. [Figure 8] 10 shows a table of simulation results for a three-terminal network according to one embodiment of the present disclosure. [Figure 9] 10 shows the percentage error of a parameter calculated based on a method according to one embodiment of the present disclosure. [Figure 10] 1 shows a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 11] 1 shows a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 12] 1 shows a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 13] 1 illustrates a graphical simulation result of a three-terminal network according to one embodiment of the present disclosure. [Figure 14] 10 shows a table of simulation results for a three-terminal network according to one embodiment of the present disclosure. [Figure 15] 10 shows the percentage error of a parameter calculated based on a method according to one embodiment of the present disclosure. [Figure 16] FIG. 1 is a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 17] 1 illustrates a graphical simulation result of a three-terminal network according to one embodiment of the present disclosure. [Figure 18] 10 shows a table of simulation results for a three-terminal network according to one embodiment of the present disclosure. [Figure 19] FIG. 1 is a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 20] 1 illustrates a graphical simulation result of a three-terminal network according to one embodiment of the present disclosure. [Figure 21]10 shows a table of simulation results for a three-terminal network according to one embodiment of the present disclosure. [Figure 22] FIG. 1 is a diagram of a three-terminal network according to an embodiment of the present disclosure. [Figure 23] 1 illustrates a graphical simulation result of a three-terminal network according to one embodiment of the present disclosure. [Figure 24] 10 shows a table of simulation results for a three-terminal network according to one embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0064] Detailed Description of Disclosure FIG. 1a shows a flowchart of a method according to one embodiment of the present disclosure. In particular, the flowchart illustrates a two-stage method for a network including a power line terminated by at least three terminals, the at least three terminals terminating the power line at each end of the power line, the power line including respective sections that are portions of the power line from a location on the power line to each end, and at least one electrical parameter of each section differs in value from the electrical parameters of each of the other sections. Such a network is also referred to as a network with mixed lines. A network in which the electrical parameters of all respective sections are equal in value may also be referred to as a network with uniform lines. The power line may be a transmission line. A terminal may refer to a conductor, particularly a transmission line, or a point where a network terminates. A terminal may also refer to an electrical connector at this end, acting as an interface to further conductors and creating a point to which an external circuit can be connected. A terminal may also be an electrical bus, particularly a busbar and / or bus duct, used to connect high-voltage equipment. A transmission line may be connected to a load or source via a terminal that terminates the transmission line. In S101, pre-fault voltages and currents from all terminals, i.e., three terminals in this embodiment, are obtained, which may be available using digital fault recorder (DFR) data. This data can be periodically recorded by the IED for analysis. Those skilled in the art will understand that the power line may be further terminated by a fourth terminal coupled to a fourth power source, a fifth terminal coupled to a fifth power source, and so on. In S102, a two-stage method algorithm is implemented. In step 1, the series impedance of each section is calculated using a first model of the network, e.g., an RL model. In step 2, the series impedance obtained from step 1 is provided as an initial guess for the least squares method, and further line parameters are estimated using a second model of the network, e.g., a distributed parameter model.The further line parameters calculated in step 2 may be the same as, and particularly with higher accuracy, the parameters calculated in step 1. In S103, the line parameters are output for further use in systems including, among other things, protection, control, and fault location applications.

[0065] FIG. 1b shows a flowchart of a method according to one embodiment of the present disclosure. At S151, measurements, particularly measurements taken before a fault, are obtained for at least three terminals terminating a power line at each end of the power line, the power line including respective sections that are portions of the power line from a location on the power line to each end, and at least one electrical parameter of each section differs from the electrical parameter of each of the other sections. It will be understood by those skilled in the art that measurements before a fault may also refer to measurements performed in the absence of a fault, i.e., in the absence of a fault. At S152, at least one input parameter for a network model of the network is obtained based on the obtained measurements of the at least three terminals, the at least one input parameter for the network model being an electrical parameter of the network model, particularly the impedance of one of the respective sections of the power line. At S153, the at least one network parameter is determined based on the at least one input parameter for the network model and the network model. At S154, the at least one network parameter is provided to a device configured to control, monitor, and / or analyze the network.

[0066] According to one embodiment, obtaining at least one input parameter for the network model includes or is determining at least one input parameter for the network model based on the obtained measurements of the at least three terminals and a further network model, the further network model being different from the network model used to determine the at least one network parameter, and the network model including at least one more electrical parameter than the further network model, in particular a propagation constant of one of the respective sections of the power line or a line capacitance of one of the respective sections of the power line coupling one of the respective sections to an electrical ground potential.

[0067] According to one embodiment, at least one input parameter for the network model is determined adaptively to differences in electrical parameters between respective sections of the power line modeled with the further network model, and / or at least one network parameter is determined adaptively to differences in electrical parameters between respective sections of the power line modeled with the further network model.

[0068] According to one embodiment, the method further includes determining a faulted section based on at least one input parameter for the network model, and controlling an auto-reclosing device for a power device, in particular a power line, based on the determined faulted section.

[0069] According to one embodiment, the method further includes estimating a fault location based on the determined faulted section, at least one electrical parameter of the network model, and particularly voltage and current fault phasors measured during the fault, particularly when the power device operates in a first operating mode in response to the control, and providing at least one network parameter to a device configured to control, monitor, and / or analyze the network.

[0070] 2 shows a diagram of a three-terminal network according to one embodiment of the present disclosure. In particular, network 200 comprises a power line terminated at each end by three terminals: bus M231, bus N232, and bus P233. The portions of the power line from point J to each of the three terminals 231, 232, and 233 are referred to as a first section MJ241, a second section NJ242, and a third section PJ243, respectively. Each of the three terminals 231, 232, and 233 has a power supply voltage parameter (E M , E N , δ N , E P , δ P ) and their respective source impedances Z sM 221, Z SN 222, and Z SP 223 are coupled to respective power sources 211, 212, and 213 modeled at 223. The modeled parameters of the power sources describe their operating conditions before the fault.

[0071] In the following, two scenarios are considered: 1) All sections, MJ241, NJ242, and PJ243, have the same parameters; 2) MJ241 and NJ242, also called main sections, have the same parameters, and PJ, also called tap line, has parameters that differ specifically from those of MJ241 and NJ242.

[0072] In the following, the first scenario is considered. -Scenario 1: All sections, MJ241, NJ242, and PJ243, have the same parameters.

[0073] FIG. 3 illustrates a series impedance model of a three-terminal network according to one embodiment of the present disclosure. In particular, FIG. 3 illustrates a series impedance (RL) model 300 of network 200. According to one embodiment, series impedance model 300 is used in step 1 of FIG. 1. According to one embodiment, the series impedance model is referred to as the network model of network 200. According to one embodiment, step 1 of FIG. 1 is a non-iterative method for parameter estimation. The modeled network 300 comprises a power line terminated at each end by three terminals: bus M331, bus N332, and bus P333. The parameters of the network are as follows: Z1=R1+jX1;Y1=jB1;X1=jωL1;B1=jωC1;ω=2πf; Z2=R2+jX2;Y2=jB2;X2=jωL2;B2=jωC2; V M 1 = Positive-sequence voltage measured on bus M331 I M 1 = Positive-sequence current measured on bus M331 V N 1 = Positive-sequence voltage measured on bus N332 I N 1 = Positive sequence current measured on bus N332 V P 1 = Positive-sequence voltage measured on bus P333 I P 1 = Positive sequence current measured on bus P333 Z1, Z2 = Positive-sequence series impedance of sections MJ, NJ and PJ, in Ω / m Y1, Y2 = Positive-sequence shunt admittances of sections MJ, NJ and PJ, in mho / m R1, R2 = positive sequence resistance of sections MJ, NJ and PJ, in ohms / m X1, X2 = Positive sequence inductances of sections MJ, NJ and PJ, in ohms / m B1, B2 = Positive-sequence susceptances of sections MJ, NJ and PJ, in mho / m ω = angular velocity, in radians / second f = system frequency, in Hz L1, L2 = Positive-sequence inductances of sections MJ, NJ and PJ, in H / m C1, C2 = Positive sequence capacitance of sections MJ, NJ and PJ, in F / m l MJ = length of section MJ, in meters l NJ = length of section NJ in meters l PJ = length of section PJ, in meters Considering scenario 1, all sections have the same parameters, so Z2=Z1.

[0074] From Figure 3, when applying Kirchhoff voltage law (KVL) between MPs, the result is as follows:

[0075]

number

[0076] Similarly, when KVL is applied between NPs, we get:

[0077]

number

[0078] From the above equations (1) and (2), Z1 is calculated as follows:

[0079]

number

[0080] Substituting Z1 into equation (2), Z2 is given as follows:

[0081]

number

[0082] Here, Z2=Z1 since all sections have the same parameters. FIG. 4 illustrates a distributed (RLC) model of a three-terminal network according to one embodiment of the present disclosure. In particular, FIG. 4 illustrates a distributed parameter model 400 of network 200. According to one embodiment, approximate model 400 is used in step 2 of FIG. 1. According to one embodiment, the distributed model is referred to as a further network model of network 200. According to one embodiment, step 2 of FIG. 1 is an iterative method, in particular a least-squares iteration method, or a root-finding algorithm, such as Newton's method, for parameter estimation. According to one embodiment, the parameters obtained from step 1, in particular using the model of FIG. 3, are provided as initial guesses for step 2, in particular using the model of FIG. 4. The modeled network 400 comprises a power line terminated at each end by three terminals: bus M 431, bus N 432, and bus P 433. The parameters of the network are as follows:

[0083]

number

[0084] Z chMJ 1 =Z chNJ 1 = Characteristic impedance of the main line Z chPJ 1 = characteristic impedance of tapped line gamma MJ =γ NJ = propagation constant of the main line gamma PJ = Propagation constant of tap line In the first scenario, i.e., considering that all sections have the same parameters, Z chPJ 1=Z chMJ 1 and γ PJ =γ MJ The initial guesses for the following method, i.e., least squares iteration, may be provided from step 1 as follows: R and L from Z1 are taken as initial guesses, and C is varied from -50% to +50% of the actual value, i.e.,

[0085]

number

[0086] The ABCD parameters of each section are described as follows:

[0087]

number

[0088] The ABCD parameters are the junction voltage V JM ,V JN , and V JP and current I JM ,I JN , and I JP to the measured voltages and currents at terminals 431, 432, and 433 as follows:

[0089]

number

[0090] By setting the junction voltages equal as calculated from terminals M431 and P433, V JM -V JP =0,

[0091]

number

[0092] Substituting equations (5) to (7) into equation (11), we obtain the following equation.

[0093]

number

[0094] By setting the junction voltages equal as calculated from terminals N and P, V JN -V JP =0,

[0095]

number

[0096] Substituting equations (5) to (7) into equation (13), we obtain the following equation.

[0097]

number

[0098] Applying KCL to the junction J, we get:

[0099]

number

[0100] From equations (8) to (10), I MJ ,I NJ and I PJ is calculated as follows:

[0101]

number

[0102] Equations (12), (14), and (15) are of the form F(X)=0, so the objective function is formulated as:

[0103]

number

[0104] Each objective function is split into real and imaginary terms and solved using least squares iteration. The unknowns from the nonlinear equations above are R1, X1, and B1. Objective function F1 3T and F3 3T is used to solve for the unknowns. The line parameters are obtained as follows:

[0105]

number

[0106] FIG. 5 illustrates a flowchart of a method according to an embodiment of the present disclosure. FIG. 5 may be a detailed embodiment of FIG. 1. At 511, voltage and current measurements from all terminals are recorded. The voltage and current measurements from all terminals may be acquired, received, stored, etc. At 512, the availability of initial guesses is determined. If not, at 513, power line parameters are calculated using an RL model of the network. If yes, the initial guesses, particularly the line parameters, are provided directly to 514. At 514, further parameters are estimated using a distributed model of the network based on the line parameters from the previous step. According to one embodiment, the determination of 512 is omitted, and the recorded voltage and current measurements from all terminals are provided directly to 513. According to one embodiment, 513 is omitted, and the initial guesses and / or recorded voltage and current measurements from all terminals are provided directly to 514. The line parameters estimated at 514 may be more accurate than the line parameters calculated at 513. At 513, parameters are calculated based on the difference 531 of the parameters of the three sections, based on equation (3) 535 or equation (3) and equation (4) 536. Similarly, at 514, parameters are calculated based on the difference 541 of the parameters of the three sections, based on equations (19) and (21) 545 or equations (19) through (21) 546. For example, at block 545, F1 according to equations (19) and (21), respectively, is calculated. 3T and F3 3Tcan be solved for the line parameters, and in block 546, F1 3T ,F2 3T , and F3 3T can be solved for the line parameters. The line parameters, whether they come from an initial guess or are calculated in 513, are fed to 521 where the faulted section is identified. In 522 it is determined whether the fault is in the overhead line. If not, auto-reclosing is blocked in 523, i.e., the action, behavior, etc. is disabled. If yes, auto-reclosing is enabled in 524. It is then determined in 525 whether auto-reclosing was successful. If yes, the algorithm ends. If no, 515 is executed. According to one embodiment, 514 and 520 are performed simultaneously.

[0107] 6 shows a diagram of a three-terminal network according to one embodiment of the present disclosure. In particular, network 600 comprises a power line terminated at each end by three terminals: bus M 631, bus N 632, and bus P 633. The portions of the power line from point J to each of the three terminals 631, 632, and 633 are referred to as first section MJ 641, second section NJ 642, and third section PJ 643, respectively. Each of the three terminals 631, 632, and 633 is coupled to a respective power source 611, 612, and 613. First power source 611 and second power source 612 are conventional power sources, including, but not limited to, synchronous generators. The third power source 613 is a non-conventional power source including, but not limited to, an asynchronous generator, more specifically, a Type IV wind turbine generator (WTG), and is coupled to the third terminal 633 via a first transformer 661 and a second transformer 662. According to one embodiment, the first transformer 661 and the second transformer 662 are omitted.

[0108] Network 600 is simulated with an EMTDC (Electromagnetic Transients including DC) tool. The proposed algorithm is implemented in a MATLAB script. The method according to one embodiment of the present disclosure is implemented on a 220 kV, 50 Hz network 600, particularly according to the flowchart in FIG. 5, with line lengths of each section of MJ = 80 km, NJ = 40 km, and PJ = 20 km. Tables 691, 692, and 693 show the source parameters, line parameters, and type IV WTG parameters, respectively. Simulation results considering all three sections MJ 641, NJ 642, and PJ 643 with the same parameters and WTG 613 at full load are shown in FIGS. 7, 8, and 9.

[0109] Figure 7 shows graphical simulation results of a three-terminal network according to one embodiment of the present disclosure. In particular, Figure 7 shows that voltage and current phasors are obtained using a discrete Fourier transform. Figure 8 shows a table of simulation results of a three-terminal network according to one embodiment of the present disclosure.

[0110] With reference to FIG. 1a) and FIG. 5, the following illustrates a method according to one embodiment of the present disclosure, where it is assumed that no initial guesses are available, i.e. the line parameters input in 514 are calculated using an RL model in 513.

[0111] In the following, the first scenario is considered. -Scenario 1: All sections, MJ641, NJ642, and PJ643, have the same parameters.

[0112] · Step 1: Calculate initial guess value 513. Z1 is calculated using equation (3) as follows:

[0113]

number

[0114] · Step 2: Estimation of line parameters514. The parameters obtained from step 1 are given as initial guesses to the least squares iteration:

[0115]

number

[0116] where v0 represents the initial guess calculated in step 1 above. The unknown vectors are estimated using least squares as follows:

[0117]

number

[0118] The estimated parameters are obtained using R1=R1; L1=X1 / ω; C1=B1 / ω as follows:

[0119]

number

[0120] The percentage error for each parameter can be calculated as follows:

[0121]

number

[0122] FIG. 9 shows the percentage error of the parameters calculated based on a method according to one embodiment of the present disclosure.

[0123] In the following, the second scenario is considered. -Scenario 2: MJ641 and NJ642 have the same parameters, and PJ643 has parameters different from those of MJ641 and NJ642. In particular, the main line 641 and 642 sections are considered as overhead lines, and PJ, which is a tap line, is considered as an underground cable.

[0124] Step 1: Initial guess calculation 513. In particular, the track parameters are calculated at 536. · Step 2: Estimation of line parameters514.

[0125] The initial guesses for the least squares iteration are provided from step 1 as follows: The following R and L from Z1 and Z2 are taken as initial guesses, and C is varied from -50% to +50% of the actual value:

[0126]

number

[0127] Each objective function is split into real and imaginary parts and solved using least squares iteration. The unknowns from the above nonlinear equations are R1, X1, B1, R2, X2, and B2. Objective function F1 3T ~F3 3T (Equations (19) to (21)) are used to solve for the unknowns. The line parameters are obtained as follows:

[0128]

number

[0129] Below, a method according to one embodiment, in particular a method following the logic of FIG. 2, is tested in the following configurations: 1) conventional power sources at all terminals (e.g., FIG. 10); 2) a type IV wind farm at terminal P (e.g., FIG. 11); 3) a solar power plant at terminal N and a type IV wind farm at terminal P (e.g., FIG. 12).

[0130] FIG. 10 shows a diagram of a three-terminal network according to one embodiment of the present disclosure. In particular, network 1000 comprises a power line terminated at each end by three terminals: bus M 1031, bus N 1032, and bus P 1033. The portions of the power line from point J to each of the three terminals 1031, 1032, and 1033 are referred to as first section MJ 1041, second section NJ 1042, and third section PJ 1043, respectively. Each of the three terminals 1031, 1032, and 1033 is coupled to a respective power source 1011, 1012, and 1013. First power source 1011, second power source 1012, and third power source 1013 are conventional power sources, including, but not limited to, synchronous generators. Tables 1091 and 1092 show source parameters and line parameters (positive sequence).

[0131] 11 shows a diagram of a three-terminal network according to one embodiment of the present disclosure. In particular, network 1100 comprises a power line terminated at each end by three terminals: bus M 1131, bus N 1132, and bus P 1133. The portions of the power line from point J to each of the three terminals 1131, 1132, and 1133 are referred to as first section MJ 1141, second section NJ 1142, and third section PJ 1143, respectively. Each of the three terminals 1131, 1132, and 1133 is coupled to a respective power source 1111, 1112, and 1113. First power source 1111 and second power source 1112 are conventional power sources, including, but not limited to, synchronous generators. The third power source 1113 is a non-conventional power source including, but not limited to, an asynchronous generator, more specifically, a Type IV wind turbine generator WTG, and is coupled to the third terminal 1133 via a first transformer 1161 and a second transformer 1162. According to one embodiment, the first transformer 1161 and the second transformer 1162 are omitted. Tables 1191, 1192, and 1193 show power source parameters, line parameters (positive sequence), and Type IV WTG parameters, respectively.

[0132] FIG. 12 shows a diagram of a three-terminal network according to one embodiment of the present disclosure. In particular, network 1200 comprises a power line terminated at each end by three terminals: bus M1231, bus N1232, and bus P1233. The portions of the power line from point J to each of the three terminals 1231, 1232, and 1233 are referred to as first section MJ1241, second section NJ1242, and third section PJ1243, respectively. Each of the three terminals 1231, 1232, and 1233 is coupled to a respective power source 1211, 1212, and 1213. First power source 1211 is a conventional power source, including, but not limited to, a synchronous generator. Second power source 1212 is a non-conventional power source, including, but not limited to, an asynchronous generator, more specifically, a solar power plant. The third power source 1213 is a non-conventional power source including, but not limited to, an asynchronous generator, more specifically, a type IV wind turbine generator WTG, and is coupled to the third terminal 1233 via a first transformer 1261 and a second transformer 1262. According to one embodiment, the first transformer 1261 and the second transformer 1262 are omitted. Tables 1291, 1292, 1293, and 1294 show power source parameters, line parameters (positive sequence), type IV WTG parameters, and solar power plant parameters, respectively.

[0133] 13-15 show simulation results obtained considering the network 1100 of FIG. 11. FIG. 13 shows graphical simulation results of a three-terminal network according to one embodiment of the present disclosure. In particular, FIG. 13 shows voltage and current phasors obtained using a discrete Fourier transform. FIG. 14 shows a table of simulation results of a three-terminal network according to one embodiment of the present disclosure. FIG. 15 shows the percentage error of parameters calculated based on a method according to one embodiment of the present disclosure.

[0134] The following describes an embodiment following FIG. 5 for the network 1100 of FIG. · Step 1: Calculate initial guess value 513.

[0135] Z1 is calculated using equation (3) as follows:

[0136]

number

[0137] Z2 is then calculated using equation (4) as follows:

[0138]

number

[0139] · Step 2: Estimation of line parameters514. The parameters (R, L) obtained from step 1 are fed into the least squares iteration as initial guesses.

[0140]

number

[0141] The unknown vectors are estimated using the least squares method.

[0142]

number

[0143] The estimated parameters are obtained using equation (33) as follows:

[0144]

number

[0145] The percentage error for each parameter can be calculated as follows:

[0146]

number

[0147] FIG. 15 shows the percentage error of the parameters calculated based on a method according to one embodiment of the present disclosure.

[0148] 17 and 18 show simulation results obtained considering the network of FIG. 16 with an AG fault at F1 on a 25% (5 km) PJ section of the line from bus P with a fault resistance of 2 Ω. According to one embodiment, the network of FIG. 16 is network 1000 of FIG. 10. FIG. 17 shows graphical simulation results of a three-terminal network according to one embodiment of the present disclosure. In particular, FIG. 17 shows voltage and current phasors obtained using a discrete Fourier transform. FIG. 18 shows a table of simulation results of a three-terminal network according to one embodiment of the present disclosure.

[0149] The following describes an embodiment following FIG. 5 for the network of FIG. · Step 1: Calculate initial guess value 513.

[0150] Z1 is calculated using equation (3) as follows:

[0151]

number

[0152] Z2 is then calculated using equation (4) as follows:

[0153]

number

[0154] · Step 2: Estimation of line parameters514. The parameters (R, L) obtained from step 1 are fed into the least squares iteration as initial guesses.

[0155]

number

[0156] The unknown vectors are estimated using the least squares method.

[0157]

number

[0158] The estimated parameters are obtained using equation (33) as follows:

[0159]

number

[0160] The percentage error for each parameter can be calculated as follows:

[0161]

number

[0162] According to one embodiment, an auto-reclosing protection scheme is implemented. According to one embodiment, the faulted section is identified as "Section PJ." According to one embodiment, the corresponding fault loop is performed from the faulted section information, and the fault location is calculated as 5.01 km from bus M. According to one embodiment, the absolute percentage of the fault location error is 0.01% for a simulated 120 km transmission line.

[0163] 20 and 21 show simulation results obtained considering the network of FIG. 19 with an AB fault F2 on 87.5% (70 km) of the line MJ section from bus M with a fault resistance of 10 Ω. According to one embodiment, the network of FIG. 19 is network 1100 of FIG. 11. FIG. 20 shows graphical simulation results of a three-terminal network according to one embodiment of the present disclosure. In particular, FIG. 20 shows voltage and current phasors obtained using a discrete Fourier transform. FIG. 21 shows a table of simulation results of a three-terminal network according to one embodiment of the present disclosure.

[0164] · Step 1: Calculate initial guess value 513. Z1 is calculated using equation (3) as follows:

[0165]

number

[0166] Z2 is then calculated using equation (4) as follows:

[0167]

number

[0168] · Step 2: Estimation of line parameters514. The parameters (R, L) obtained from step 1 are fed into the least squares iteration as initial guesses.

[0169]

number

[0170] The unknown vectors are estimated using the least squares method.

[0171]

number

[0172] The estimated parameters are obtained using equation (33) as follows:

[0173]

number

[0174] The percentage error for each parameter can be calculated as follows:

[0175]

number

[0176] According to one embodiment, an auto-reclosing protection scheme is implemented. According to one embodiment, the faulted section is identified as "Section MJ." According to one embodiment, the corresponding fault loop is performed from the faulted section information, and the fault location is calculated as 69.90 km from Bus M. According to one embodiment, the absolute percentage of the fault location error is 0.01% for the simulated 120 km transmission line.

[0177] 23 and 24 show simulation results obtained considering the network of FIG. 22 with a BCG fault on the NJ section 105 km from bus M with a fault resistance of 20 Ω. According to one embodiment, the network of FIG. 22 is network 1200 of FIG. 12. FIG. 23 shows graphical simulation results of a three-terminal network according to one embodiment of the present disclosure. In particular, FIG. 23 shows voltage and current phasors obtained using a discrete Fourier transform. FIG. 24 shows a table of simulation results of a three-terminal network according to one embodiment of the present disclosure.

[0178] · Step 1: Calculate initial guess value 513. Z1 is calculated using equation (3) as follows:

[0179]

number

[0180] Z2 is calculated using equation (4) as follows:

[0181]

number

[0182] · Step 2: Estimation of line parameters514. The parameters (R, L) obtained from step 1 are fed into the least squares iteration as initial guesses.

[0183]

number

[0184] The unknown vectors are estimated using the least squares method.

[0185]

number

[0186] The estimated parameters are obtained using equation (33) as follows:

[0187]

number

[0188] The percentage error for each parameter can be calculated as follows:

[0189]

number

[0190] According to one embodiment, an auto-reclosing protection scheme is implemented. According to one embodiment, the faulted section is identified as "Section NJ." According to one embodiment, the corresponding fault loop is performed from the faulted section information, and the fault location is calculated as 105.08 km from Bus M. According to one embodiment, the absolute percentage of the fault location error is 0.08% for the simulated 120 km transmission line.

[0191] 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 other embodiments described herein. Thus, the breadth and scope of the present disclosure should not be limited by any of the above-described example embodiments.

[0192] It will also be understood that any reference to an element herein using a designation 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 used or that the first element must in any way precede the second element.

[0193] 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.

[0194] 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.

[0195] 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.

[0196] 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 can 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 can further include an antenna and / or transceiver for communicating with various components within a network or device. The general-purpose processor can be a microprocessor, although in the alternative, the processor can be any conventional processor, controller, or state machine. A processor can also be implemented as a combination of computing devices, e.g., 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 can 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.

[0197] Computer-readable media includes both computer storage media and communication media, including any medium that can enable a computer program or code to be transferred 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.

[0198] Additionally, memory or other storage devices, as well as communication components, may be used 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, functions shown to be 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 indicate a strict logical or physical structure or organization, but merely to suitable means for providing the described functionality.

[0199] 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 the present disclosure. Thus, the present disclosure is not intended to be limited to the embodiments 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 determining at least one network parameter of a network comprising a power line terminated by at least three terminals, comprising: obtaining measurements of at least three terminals terminating the power line at respective ends of the power line, the power line comprising respective sections that are portions of the power line from a location on the power line to the respective ends; the measurements are taken before the failure; obtaining at least one electrical parameter of the respective sections that is different from the electrical parameter of each other section; obtaining at least one input parameter for a network model of the network based on the obtained measurements of at least three of the terminals; - obtaining the at least one input parameter for the network model, which is an electrical parameter of the network model, in particular an impedance of one of the respective sections of the power line; determining the at least one network parameter based on the at least one input parameter for the network model and the network model; providing the at least one network parameter to a device configured to control, monitor, and / or analyze the network; A method comprising:

2. obtaining the at least one input parameter for the network model includes or is determining the at least one input parameter for the network model based on the obtained measurements of at least three of the terminals and a further network model; the further network model is different from the network model used to determine the at least one network parameter; 2. The method of claim 1, wherein the network model includes at least one more electrical parameter than the further network model, in particular a propagation constant of one of the respective sections of the power line or a line capacitance of one of the respective sections of the power line coupling one of the respective sections to electrical ground potential.

3. 3. The method of claim 2, wherein the at least one input parameter for the network model is determined adaptively to differences in electrical parameters between the sections of each of the power lines modeled with the further network model, and / or the at least one network parameter is determined adaptively to differences in electrical parameters between the sections of each of the power lines modeled with the further network model.

4. determining a faulty section based on the at least one input parameter for the network model; and controlling a power device, in particular an automatic reclosing device for the power line, based on the determined faulty section; The method of any one of claims 1 to 3, further comprising:

5. estimating a fault location based on the determined faulted section, at least one electrical parameter of the network model, and particularly voltage and current fault phasors measured during the fault, particularly when the power device operates in a first operating mode in response to the control; providing said at least one network parameter to said device configured to control, monitor, and / or analyze said network; The method of claim 4 further comprising:

6. 1. An apparatus for determining at least one network parameter of a network comprising a power line terminated by at least three terminals, the apparatus comprising: a processor; obtaining measurements of at least three terminals terminating the power line at respective ends of the power line, the power line comprising respective sections that are portions of the power line from a location on the power line to the respective ends; the measurement is taken prior to the failure; obtaining at least one electrical parameter of the respective sections that is different from the electrical parameter of each other section; obtaining at least one input parameter for a network model of the network based on the obtained measurements of at least three of the terminals; - obtaining the at least one input parameter for the network model, which is an electrical parameter of the network model, in particular an impedance of one of the respective sections of the power line; determining the at least one network parameter based on the at least one input parameter for the network model and the network model; providing the at least one network parameter to a device configured to control, monitor, and / or analyze the network; 11. An apparatus comprising: a processor configured to:

7. the processor is configured to obtain the at least one input parameter for the network model by determining the at least one input parameter for the network model based on the obtained measurements of at least three of the terminals and a further network model; the further network model is different from the network model used to determine the at least one network parameter; 7. The apparatus of claim 6, wherein the network model includes at least one more electrical parameter than the further network model, in particular a propagation constant of one of the respective sections of the power line or a line capacitance of one of the respective sections of the power line coupling one of the respective sections to electrical ground potential.

8. 8. The apparatus of claim 7, wherein the processor is configured to determine the at least one input parameter for the network model adaptively to differences in electrical parameters between the sections of each of the power lines modeled with the further network model, and / or the processor is configured to determine the at least one network parameter adaptively to differences in electrical parameters between the sections of each of the power lines modeled with the further network model.

9. The processor: determining a faulty section based on the at least one input parameter for the network model; and controlling a power device, in particular an automatic reclosing device for the power line, based on the determined faulty section; The apparatus of any one of claims 6 to 8, further configured to:

10. The processor: estimating a fault location based on the determined faulted section, at least one electrical parameter of the network model, and particularly voltage and current fault phasors measured during the fault, particularly when the power device operates in a first operating mode in response to the control; providing said at least one network parameter to said device configured to control, monitor, and / or analyze said network; The apparatus of claim 9 , further configured to:

11. A computer-readable medium carrying instructions for performing the method of any one of claims 1 to 5 for determining at least one network parameter of a network comprising a power line terminated by at least three terminals.

12. A system comprising a network comprising a power line terminated by at least three terminals and a device according to any one of claims 6 to 10.

13. 13. The system according to claim 12, further comprising a power device, in particular an auto-reclosing device for said power line.

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