Abstract: The invention relates to a transient based method for identifying faults in an electric power transmission and/or distribution system (100) having at least one current transmission line (L12, L13, L23) comprising the following steps: —generation of a physical model of the at least one current transmission line (L12, L13, L23), the physical model depending on the fault parameters and describing the behavior of voltage and/or current transients due to the fault in the at least one current transmission line, fault parameters comprising a fault location parameter on said current transmission line (L12, L13, L23) and a fault impedance parameter, —measurement of voltage and/or currents evolution at least at one specific location in the said power system (100), —iterative simulation of the voltage and/or current evolution by the physical model at the measurement point with a set of fault parameters where at each step of iteration, simulated and measured voltage and/or current evolutions are compared and the set of f

Abstract: A method identifies a diagnosis variable which indicates an aging state of an operating device in an electrical energy supply network. In the method, first measurement values of at least one measurement variable are detected at a first measuring point of the operating device. Then simultaneously second measurement values of the at least one measurement variable are detected at a second measuring point of the operating device. The diagnosis variable is identified using respective simultaneously detected first and second measurement values. It is proposed that the first and second measurement values are detected in a time-controlled manner in such a way that a signal of the at least one measurement variable is sampled at a prescribed sampling rate at set times and over a set measurement duration so as to generate time profiles of the first and second measurement values.

Abstract: A fault location system in a cable transport installation comprises a safety unit (10) and an end module (13) connected by an electrical safety line (11). The safety line (11) comprises a plurality of cable fault contacts (14) of the normally-closed type connected in series. The location system includes a plurality of location modules (20) distributed along the transport installation, each of which comprising a first test contact (21), of the normally-open type, for short-circuiting the safety line (11). Once a fault coming from one of the cable fault contacts (14) is detected, each location module (20) is capable of selectively closing its first test contact (21) so as to be able to locate said faulty contact (14) on the safety line.

Abstract: Electric power is transferred to an electric load as alternating current over at least two incoming and outgoing lines. At least one line circuit manages at least one parameter of the transferred electric power. A central circuit exchanges data and/or commands with the at least one line circuit over a respective galvanically isolated communication interface, such that a reference potential of the central circuit is floating relative to an earth potential of the at least two incoming and outgoing lines. A respective surge protection capacitor is arranged in parallel with each galvanically isolated communication interface. The surge protection capacitors are configured to accumulate a respective fraction of an electric charge resulting from an undesired overvoltage on one of said incoming lines so as to split up the undesired overvoltage into two or more voltages over the galvanically isolated communication interfaces each of which voltage is smaller than the undesired overvoltage.

Abstract: A method for locating phase faults in a microgrid in off-grid mode. The method includes obtaining a grid topology of the microgrid having at least two busbars and determining the position of all circuit breaker position of the grid topology. Further, acquiring measurement data which includes current magnitude and voltage magnitude. Monitoring the at least two busbars for a voltage dip in one of phase-to-phase or phase-to-neutral voltages. On detecting a voltage dip, determining a defect phase having a minimum phase-to-neutral voltage value. And for the defect phase performing busbar analysis and feeder analysis, using phase-directional information.

Abstract: A deterioration degree diagnosis device includes a measurement unit and a diagnosis unit. The measurement unit measures an impedance related to a contact resistance of an electrical connection portion by measuring an AC voltage between metal members and an AC current flowing between the metal members in a state where an AC signal of a predetermined frequency is applied to an electric circuit that connects two metal members in contact via the electrical connection portion. The diagnosis unit diagnoses a deterioration degree of the electrical connection portion based on a reactance component value in the impedance measured by the measurement unit.

Abstract: The present invention relates to a method of monitoring oscillations that are liable to interact in an electrical power network, in dependence on measurement of AC waveforms in the electrical power network. The method comprises receiving first waveform data corresponding to an electrical quantity in each phase of at least two phases of three-phase AC waveforms at a location in the electrical power network. The method further comprises applying a transformation to the first waveform data to provide therefrom second waveform data corresponding to an electrical quantity at the location in a single phase representation, the second waveform data depending on the at least two phases.

Abstract: A method for detecting an electric leakage point without interrupting a power supply is provided. The method includes transmitting a unipolar direct current (DC) survey voltage signal to an electric wire of the power supply. The method includes transmitting a chain of electromagnetic wave signals generated around the electric wire to synchronize a reference time to measure an earth potential of the unipolar DC voltage signal and capture an electromagnetic tracking signal. The method includes tracing a buried route of the electric wire by analyzing the electromagnetic tracking signal according to the reference time. The method includes measuring the earth potential of the unipolar DC voltage signal on the ground according to the reference time. The method includes locating the electric leakage point by identifying a polarity of the unipolar DC voltage signal.

Abstract: A device for detecting an electrical load connected to an electric power supply network. The device comprises means for injecting a test signal into the electrical network and means for identifying the presence and the nature of an electrical load connected to the electrical network on the basis of the test signal.

Abstract: A ground fault overvoltage relay device is configured to: determine whether or not a first condition is satisfied, the first condition being that at least two of line voltages between respective two phases are less than or equal to a first threshold value; determine whether or not a second condition is satisfied, the second condition being that a ratio between a minimum value of the line voltages between the respective two phases and a minimum value of the respective phase voltages is less than or equal to a second threshold value; determine whether or not a third condition is satisfied, the third condition being that the zero-phase voltage is greater than a third threshold value; and lock a ground fault detection output when the first condition is satisfied, or when the second condition is satisfied and the third condition is not satisfied.

Abstract: The present disclosure relates to a computationally efficient technique for determining a location of a fault on a power line using local measurements and remote current measurements. For example, a method may include receiving one or more local measurements of a power line. The method includes receiving a signal indicating one or more remote current measurements of the power line. The method includes determining a location of a fault on the power line based on a fault voltage multiplied by a conjugate of a compensated differential current. The method includes providing the location of the fault.

Abstract: A fault location of a fault on a line of an electrical energy supply network is determined from measured current and voltage values at the first and second line ends. Highly accurate fault location with measured values from both line ends is provided even in the absence of temporal synchronization of the measurements at the line ends. Characteristics of first and second fictitious fault voltage values present at a fictitious fault location on the line are defined using the first and second current and voltage values. A fictitious fault location is determined for which the characteristic of the first fictitious fault voltage values corresponds most closely to the characteristic of the second fictitious fault voltage values. The fictitious fault location is used as the actual fault location. We also describe a correspondingly configured device and a system for determining a fault location.

Abstract: Disclosed herein are a variety of systems and methods related to detection of a cross-country fault in an electrical power system. In one embodiment, a system consistent with the present disclosure may be configured to monitor electrical parameters in the electrical power system. The system may determine when a voltage magnitude of one phase exceeds a first voltage threshold. The one phase that exceeds the first voltage threshold may be identified as an un-faulted phase. The system may further be configured to determine that the voltage magnitude of the un-faulted phase exceeds a second threshold based on a zero-sequence voltage. The system may further be configured to determine that a phase angle between the un-faulted phase and the zero-sequence voltage is within a range. A protective action to clear the cross-country fault condition may be implemented upon identification of a cross-country fault.

Abstract: An electric arc detection apparatus includes: a current sensor; a first filter; a second filter; an FFT processing portion that generates a high-frequency power spectrum and a low-frequency power spectrum; an electric arc detection portion that detects an electric arc by using the high-frequency power spectrum; a pseudo electric arc mask portion that determines a pseudo electric arc by using the low-frequency power spectrum; and an electric arc presence/absence determining portion.

Abstract: A circuit for evaluating measurement signals of at least one sensor with a control circuit. A control signal having a first frequency is generated by a control section of the control circuit, and the control signal is applied to the sensor. An electronic evaluation unit is provided for generating an evaluation signal originating from a measurement signal generated by the sensor. The electronic evaluation unit generates an opposing signal having the first frequency and a modifiable phase angle and superposes the opposing signal and the evaluation signal. The signal resulting from the superposition of the opposing signal and the evaluation signal is fed to a synchronous demodulator of the electronic evaluation unit.

Abstract: A power supply protection device including a driving circuit, a logic control unit and a protection module is provided. The driving circuit adjusts an external voltage according to a first driving signal and a second driving signal and outputs a driving voltage. The logic control unit generates the first driving signal and the second driving signal according to a protection signal and a pulse signal. The protection module outputs a plurality of test currents orderly to detect a plurality of impedances of the driving circuit before the driving circuit receives the external voltage, generates a plurality of voltage signals according to the impedances and compares the voltage signals with a plurality of reference voltages to generate the protection signal. A power supply protecting method for protecting a driving circuit is also provided.

Abstract: A method for identifying the type of faults occurred on a power line, characterized in that it comprises: calculating a fault point voltage on fault points based on terminal voltage and fault locations of the power line; adopting the fault point voltage corresponding to a maximum transition resistance as a setting value; comparing the fault point voltage on fault points with the setting value; and identifying the type of fault as a permanent type or a transient type based on the result of the comparison.

Abstract: The present invention relates to a method for assessment of a power system and an early warning system for a power system, the method being based on aperiodic small signal instabilities. The power system has a plurality of generators comprising one or more synchronous machines and is represented by a plurality of nodes of power injection, injecting power into a network having a plurality of nodes and branches. The method for assessment of the power system comprises determining a present state of the power system, calculating system Thevenin impedances from each node of power injection in the power system on the basis of the determined present state of the power system, calculating injection impedances from each node of power injection in the power system on the basis of the determined present state of the power system, determining a stability boundary for each generator based on the calculated system Thevenin impedances and the calculated injection impedances.

Abstract: Unique systems, methods, techniques and apparatuses of fault location in DC power distribution systems are disclosed. One exemplary embodiment is a DC power distribution system including a plurality of zones each including a DC power distribution line and a protective device. Each protective device structured to sense one or more electrical characteristics of a line and to controllably open a circuit including the line. At least one intelligent electronic device is structured to determine a line inductance based upon electrical characteristics sensed by one or more of the protective devices and to evaluate a location of the line fault based upon the determined line inductance.

Abstract: A method for performing diagnostics on a transformer includes generating, by a voltage generator, an AC voltage and applying the AC voltage to a winding or phase of the transformer. Current flowing from the generator to the winding or phase is decomposed into a plurality of harmonic components. Respective magnitudes of the plurality of harmonic components are compared with corresponding magnitudes of harmonic components associated with one or more benchmark transformers of a known condition to determine whether the condition of the transformer matches the condition of one or more benchmark transformers.

Abstract: A method for determining current return path integrity in an electric device with a plurality of signal lines and supply lines. A library with at least one reference signal pattern of a near end crosstalk signal on a defined signal line arising from an input signal on another defined signal line is provided, a predetermined signal to a selected signal line of the electric device is applied, the near end crosstalk signal on at least one further signal line of the electric device is detected, said near end crosstalk signal is compared with the corresponding reference signal pattern from the library, and if there is a deviation between the near end crosstalk signal and the corresponding reference signal pattern, an information that there is any defect in the electric device is displayed.

Abstract: A system and method for detecting and locating an insulation flaw in a solar generator on a spacecraft. The solar generator comprises a plurality of flaps. Each flap bears at least one solar cell that is connected to an electrical distribution network and electrically insulated from the flap. Each flap is connected, by a first load and by a second load, to a first electrical line and a second electrical line, respectively. The ratio of the impedances of the first load and of the second load of a flap being denoted as an impedance ratio of the flap. The solar generator comprises at least two flaps exhibiting different respective impedance ratios. The system comprises a component for evaluating the currents flowing in the first and second electrical lines, and a detector for detecting and locating an insulation flaw in the solar generator based on the evaluations of the currents.

Abstract: Provided is a partial discharge detection device for a transformer, and a transformer using the same. An on-load tap changer is provided on one side of the outer casing of a transformer, and is partitioned from the inside of the outer casing by a shielding wall. A drain pipe is formed on one side of the outer surface of the outer casing. A drain valve is installed in the drain pipe. A configuration for detecting a partial discharge signal generated within the transformer is installed in the drain pipe. That is, a detector body is installed within the drain pipe and the drain valve. A connection mounting member is installed in an end portion of the drain valve. The detector body penetrates the connection mounting member. In the meantime, a portion, such as the on-load tap changer, is partitioned from the internal space of the outer casing by the shielding wall.

Abstract: A method and an apparatus are provided to reduce or eliminate interference signals that have been additively superimposed on a useful signal for locating a cable sheathing fault of a buried electrical cable. A correction unit includes a filter, a delay device and/or a DC component estimator. The correction unit automatically determines a transient interference signal and a DC offset voltage component that have been superimposed on the useful signal as received in an input signal of the correction unit, and then subtracts these determined interference signals from the input signal to provide the interference-free or interference-suppressed useful signal as the output.

Abstract: A fault detection device includes an interface electrically connected to an electrical instrument to transfer commercial power to the electrical instrument, transmit a command for driving one of a plurality of loads included in the electrical instrument to the electrical instrument, and detect current flowing in one of the plurality of loads of the electrical instrument; and a terminal configured to receive a current signal corresponding to the current flowing in one of the plurality of loads from the interface, determine whether the one load has a fault on the basis of the received current signal and display whether the load has a fault. A faulty load is determined by detecting current of only a load suspected to have a fault when a fault is generated in the electrical instrument so as to improve fault detection accuracy.

Abstract: Calculating device and method for carrying out status calculations in an electricity network (2) with a multiplicity of nodes (K1-K11). The method comprises the allocation of a local calculating agent (A1-A11) to each of the multiplicity of nodes (K1-K11), the allocation of regional calculating agents (R1, R2) to regional networks (3, 4), the reception by the regional calculating agents (R1, R2) of the results of the status calculations from the associated local calculating agents (A1-A11) and, on the basis thereof, the performance of a status calculation for the associated regional network (3, 4).

Abstract: A method and a system for three-phase detection of a three-phase electric device are provided. The system includes a testing circuit and a comparison module. The testing circuit generates two reference voltages by using the three phase voltages of the three-phase electric device. The two reference voltages are the first and second phase voltages with reference to the third phase voltage, respectively. Three-phase detection is performed by comparing the two reference voltages for a determined number of times. After testing is completed, the testing circuit is switched off by the comparison module, to save power.

Abstract: An alarm system for alarming whenever there is a power leakage from an electronic device, includes a voltage decreasing circuit, a switch circuit and an alarm circuit. The voltage decreasing circuit receives a first voltage from a live wire output terminal and outputs a second voltage. The switch circuit outputs a control signal when the power leakage is detected. The switch circuit is electrically connected to a connection port. The connection port is electrically connected to the live wire output terminal and a neutral wire output terminal. The alarm circuit receives the control signal and alarms. If there is power leakage from the electronic device, the first voltage from the live wire input terminal flows into the ground wire input terminal via the electronic device; the switch circuit turns on and the alarm circuit is closed to alarm.

Abstract: A system and method for detecting excess voltage drop (EVD) in a three-phase electrical distribution circuit includes a diagnostic system comprising a processor that is programmed to receive three-phase voltages and currents provided to terminals of the electrical machine, determine fundamental components of the three-phase voltages and currents provided to the terminals, and compute positive, negative, and zero sequence currents from the fundamental components.

Abstract: A method for detecting an internal failure in a capacitor bank connected to a power system, wherein the capacitor bank includes a plurality of capacitor units that are divided into two Y sections. Each phase in each of the Y sections defines a leg and each leg includes series and/or parallel-connected capacitor units. The internal failure may occur in one or more capacitor elements or units or involve one or more legs. The method includes measuring the phase current in one of the phases, calculating the root mean square value, denoted by RMS, of the measured phase currents, measuring the unbalanced current between the two sections, calculating the RMS value of the measured unbalanced currents, and detecting the phase angle between the measured phase current and the measured unbalanced current.

Abstract: A method of detecting a fault in a subsea power cable or in a direct electric heating system including a subsea power cable is provided. Measuring points are distributed along the subsea power cable. The method includes measuring at each measuring point a current in the subsea power cable and comparing the currents measured at the different measuring points.

Abstract: Determination of information relating to a location of an electrical fault in an electrical energy distribution system based on phasor information is disclosed. A component can receive phasor information and electrical energy distribution system information. The system can determine a distance factor based on the phasor information. The distance factor can be employed to determine fault location information. A set of fault location information can be generated. Fault location information can be corrected for fault characteristics. Equivalent circuit models can be employed in determining the distance factor. Fault locations can be validated to facilitate generating subset of fault location information. Access to fault location information can be facilitated.

Abstract: A method is provided for detection of a ground fault in a high resistance network in a voltage source power conversion circuit comprising a power converter that converts incoming AC power to DC power applied to a DC bus and an inverter that converts DC power from the DC bus to output AC power. The method includes detecting a midpoint-to-ground voltage between a low side of the DC bus and a ground potential and detecting the presence of a ground fault in a high resistance network based upon the detected midpoint-to-ground voltage.

Abstract: A method of locating incipient faults that generate partial discharges in an AC power distribution system includes detecting at least one spike in a PD pattern generated by such system; getting the voltage wave of the AC power in the system; detecting a phase of such spike with respect to the voltage of the AC power; and locating an incipient fault where such phase is below a predetermined threshold. An apparatus includes at least one sensor of electrical pulses, means for getting a synchronism signal with a power supply of the power distribution system, and modules adapted to carry out the method.

Abstract: A method for detecting an internal failure in a capacitor bank connected to a power system, wherein the capacitor bank includes a plurality of capacitor units that are divided into two Y sections. Each phase in each of the Y sections define a leg and each leg includes series and/or parallel-connected capacitor units. The internal failure may occur in one or more capacitor elements or units or involve one or more legs. The method includes measuring the phase current in one of the phases, calculating the root mean square value, denoted by RMS, of the measured phase currents, measuring the unbalance current between the two sections, calculating the RMS value of the measured unbalance currents, and detecting the phase angle between the measured phase current and the measured unbalance current.

Abstract: An apparatus and method is provided for identifying a faulted phase in at least one shunt capacitor bank. The apparatus generally includes a sampling circuit for sampling current or voltage signals associated with the shunt capacitor bank. A microcontroller is coupled to the sampling circuit and programmed to measure a compensated neutral point phase angle from the sampled signal, and compare the compensated neutral point phase angle with a fixed reference phase angle to identify the faulted phase of the shunt capacitor bank. The method generally includes the steps of sampling a current or voltage signal associated with the shunt capacitor bank, determining a compensated neutral point phase angle from the sampled signal, and comparing the compensated neutral point phase angle with a fixed reference phase angle to identify the faulted phase of the shunt capacitor bank. The invention also relates to an apparatus and method for identifying the location of the fault (e.g.

Abstract: An appliance and a method are intended to monitor a phase line of a section of an electrical energy grid line. The appliance comprises a device for monitoring a parameter of a phase line. The parameter is representative of routine operating conditions of the phase line and has a known propagation speed. The appliance also comprises a device for generating an event detection signal each time the parameter has a value that exceeds a threshold, and for storing a reception time when the detection signal is generated. The appliance also has a device for sending a signal representative of a geographic location of the end of the section and a device for performing a geographic location of the event once two consecutive detection signals are generated from the signal representative of the geographic location, and reception times associated with the two detection signals.

Abstract: According to an embodiment of the present invention, an apparatus for determining the location of an electrical disturbance in a circuit is provided. The apparatus has at least one sensor configured to determine the relative phase of current and voltage waveforms across the circuit inductance of a portion of the circuit produced by a voltage or current perturbation, and a controller configured to identify the location of the electrical disturbance within the circuit from the relative phase of the current and voltage waveforms.

Abstract: A method of determining out of step condition and an instance of separation within electrical power system. The method does not require user settings and ensures reliable discrimination between recoverable power swing and pole slips that indicates non-recoverable power swing and the need for system separation. The method also allows tripping at a user selected system angle if desired. A calculated angle is used to determine the magnitude of the swing current to control the tripping at the desired angle ? when the system could be safely split after detection of out of step condition based on the criteria of this invention.

Abstract: The present document discloses several techniques of evaluating parameters relating to noise and excess current on a power line. The techniques are particularly well-suited for characterizing partial discharge, and for identifying a location of a source of the noise or excess current.

Abstract: An apparatus and method for protecting against electrocution hazards that arise when an appliance is electrically connected to a miswired single-phase AC electrical source which includes an energized ground lead are described. The apparatus includes one or more sensors that detect electrical energy in the ground lead combined with a miswiring condition in the hot and common leads. A tester embodiment is also illustrated. The method includes the steps of detecting if the putative ground of the electrical source is energized and whether the hot and common leads are reversed.

Abstract: Embodiments of the present invention relate to methods and systems of transmitting data signals from at least one transmitting terminal with a spatial diversity capability to at least two receiving user terminals, each provided with spatial diversity receiving device. The methods and systems are useful, for example, in communication between terminals, e.g., wireless communication. In certain embodiments, transmission can be between a base station and two or more user terminals, wherein the base station and user terminals are each equipped with more than one antenna.

Abstract: A method is provided for fault location in uncompensated power lines with two-end unsynchronized measurement, finding an application in the power industry and for overhead and overhead-cable transmission or distribution lines. The method according to the invention includes measuring the voltage and currents at both ends (A) and (B) of the section, obtaining the phasor of the positive sequence voltages (VA1, VB1) measured at the ends (A) and (B), respectively, obtaining the phasor of the positive sequence currents (IA1, IB1) measured at the ends (A) and (B), respectively, determining whether there is a three-phase balanced fault, and using either a first subroutine or a second subroutine (depending on whether or not there is a fault), determining a distance (d) to the fault.

Abstract: A load compensation method for phase-to-ground loops in distance protection. A first reactive reach is estimated assuming zero fault resistance or with a positive sequence current. A second reactive reach is estimated with a zero sequence current. A third reactive reach is estimated with a negative sequence current. An import or export condition is estimated. A fourth reactive reach for import or export condition is estimated based on the first, second and third reactive reach. A fault impedance is estimated based on the estimated fourth reactive reach.

Abstract: Phase and gain of a transmit signal are measured at a transmitter by determining a first time delay having a first resolution at a measurement receiver between a reference signal from which the transmit signal is generated and a measured signal derived from the transmit signal by comparing amplitudes of the reference signal and the measured signal. A second time delay having a second resolution finer than the first resolution is determined at the measurement receiver between the reference signal and the measured signal based on the first time delay. The reference signal and the measured signal are time aligned at the measurement receiver based on the second time delay and the phase and gain of the transmit signal are estimated after the reference signal and the measured signal are time aligned.

Abstract: In order to detect, localize and interpret a partial discharge occurring in a partial discharge site along an electrical equipment, two measurement probes and a synchronization probe are installed along the electrical equipment. The measurement probes detect pulses travelling in the electrical equipment while the synchronization probe detects a phase angle in the electrical equipment and is usable for calibration purposes. A control unit receives the signals sensed by the probes and conditions them. Digital processing applied on the conditioned signals, involving their correlation, a time-frequency distribution and a form factor estimation, allows establishing a diagnosis indicating a detection of a partial discharge and its localization along the electrical equipment. A wideband magnetic probe may be provided for detecting the pulses traveling in the electrical equipment.

Abstract: A method for detecting turn-to turn faults in a laminate stack of a stator of an electrical machine or a generator includes magnetizing the stator using an auxiliary coil and an auxiliary current so as to form a magnetic field. The magnetic field is measured using a pickup device including at least two detectors disposed in at least two respective different radial positions with respect to a rotor axis so as to provide at least two signals corresponding to the magnetic field at the respective radial positions. The method includes evaluating and comparing a magnitude and/or a phase angle of the signals so as to determine a relative magnitude and/or relative phase angle by subtraction in order to detect turn-to-turn faults. Relative differences in the at least two signals are recorded. Also a device for performing the method.

Abstract: A method of detecting an output phase loss (OPHL) for a motor drive detects an abnormal OPHL operation when at least one phase of a three-phase current is continually zero. Each phase of the three-phase current is acquired, sampled, filtered, and compared. Hence, a corresponding zero-current counter value is continually added, and a corresponding abnormal current value is set as logic 1 when a zero-phase current of the three-phase current is continually zero. Finally, an OPHL certified value is set as logic 1 to confirm that the motor driver is operated in the abnormal OPHL operation. Therefore, a direct-current and an alternating-current OPHL can be detected before and after the motor driver is operated, respectively.

Abstract: The electricity distribution network comprises a plurality of interconnection lines for the distribution of electricity among a plurality of interconnection boxes. At least some of said interconnection boxes are combined with a control unit for detection of stray voltage, comprising a transmitter to transmit to a receiver of at least one collecting unit a signal relating to any dispersion.

Abstract: A method and a system for determining a circular characteristic for distance protection of a three-phase electric line, the system comprising means for detecting a fault on the electric line, means for identifying a faulted phase or phases of the electric line, means for determining, at a measuring point, a first fault loop impedance by using voltage(s) of the faulted phase(s), a second fault loop impedance by using a polarization voltage and a third fault loop impedance by using predetermined line parameters, and means for determining a radius and midpoint of the circular characteristic.