# US 2008/0189061 A1 · Real-time power-line sag monitoring using time-synchronized power system measurements > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2008/0189061 A1 - Document ID: US20080189061A1 - Status: Published application - Kind: A1 - Application number: 11/671,098 - Filed: 2007-02-05 - Published: 2008-08-07 - Earliest claimed: 2007-02-05 - Assignees: ABB Research Ltd. - Inventors: Ernst Scholtz; Reynaldo F. Nuqui; Danny Julian; Alan R. Grightmire - Web page: https://patentgrep.com/patent/US20080189061A1 ## CPC - H02G 7/02: Devices for adjusting or maintaining mechanical tension, e.g. take-up device - H02G: INSTALLATION OF ELECTRIC CABLES OR LINES, OR OF COMBINED OPTICAL AND ELECTRIC CABLES OR LINES ## Abstract A sag calculator (112) computes sag for a span of a line section based at least in part upon an average temperature of the conductors in the line section. A temperature calculator (110) determines the temperature by ascertaining an ohmic resistance of the conductor lines based at least in part upon time-synchronized power system voltage and current measurements such as (but not limited to) phasor measurements generated by phasor measurement units (104, 106). The temperature calculator (110) determines the temperature as a function of the ohmic resistance. ## Claims ### Claim 1 A computer-implemented method comprising the following computer-executable acts: receiving a conductor temperature of a power line, wherein the temperature is determined based at least in part upon time-synchronized voltage and current phasor measurements; and computing sag for a span of interest in the power line based at least in part upon the received temperature, wherein computing the sag for the span of interest comprises computing a zero tension length for a conductor of the span at a reference temperature as a function of a known length of the conductor at the reference temperature and a cross sectional area of the conductor. ### Claim 2 (depends on 1) The method of claim 1, wherein the power line includes a first end and a second end, and further comprising: receiving phasor measurements from two phasor measurement units that are positioned at the first end and the second end of the power line, respectively; and determining the temperature of the conductor in the power line as a function of the received phasor measurements. ### Claim 3 (depends on 1) The method of claim 1, further comprising: determining an ohmic resistance of the conductor in the power line; and determining the temperature as a function of the ohmic resistance. ### Claim 4 (depends on 1) The method of claim 1, further comprising computing sag for a span that is representative of multiple spans in the power line. ### Claim 5 (depends on 4) The method of claim 4, wherein the computed sag for the span of interest is determined as a function of the computed sag for the representative span. ### Claim 6 (depends on 1) The method of claim 1, wherein computing the sag for the span of interest comprises computing the sag based at least in part upon a relationship between thermal expansion of and tension in conductors in the power line. ### Claim 7 (canceled) ### Claim 8 (depends on 1) The method of claim 1, wherein computing the sag for the span of interest comprises computing a first length of the conductor at the received temperature as a function of the zero tension length for the conductor at the reference temperature, a coefficient of thermal expansion for a material of the conductor, and a difference between the reference temperature and the received temperature. ### Claim 9 (depends on 8) The method of claim 8, wherein computing the sag for the span of interest comprises calculating a first tension of the conductor at the received temperature based at least in part upon a weight per unit length of the conductor, a length of the span, and the computed first length of the conductor. ### Claim 10 (depends on 9) The method of claim 9, wherein computing the sag for the span of interest comprises computing a second length of the conductor at the received temperature as a function of the first length, the first tension, and the cross sectional area of the conductor. ### Claim 11 (depends on 10) The method of claim 10, wherein computing the sag for the span of interest comprises computing a sag of the span of interest at the received temperature as a function of the second length. ### Claim 12 (depends on 11) The method of claim 11, wherein computing the sag for the span of interest comprises computing a second tension of the conductor as a function of the computed sag of the span, the second length, and the weight per unit length of the conductor. ### Claim 13 (depends on 12) The method of claim 12, wherein computing the sag for the span of interest comprises updating the first tension of the conductor at the received temperature as a function of the first tension and the second tension. ### Claim 14 (depends on 13) The method of claim 13, wherein computing the sag for the span of interest comprises: recomputing the second length; recomputing the sag of the span of interest at the received temperature; recomputing the second tension of the conductor; determining whether the computed second length has converged; determining whether the computed second tension has converged; outputting the calculated sag of the span of interest if the computed second length and the computed second tension have converged, respectively; and updating the first tension if the computed second length and the computed second tension have not converged, respectively. ### Claim 15 (depends on 1) The method of claim 1, wherein computing the sag for the span of interest comprises including an effect of mechanical creep when determining a length and tension of a conductor in the span of interest. ### Claim 16 An apparatus, comprising: a sag calculator that computes, in real time during an operation of a power line, a sag for a span in the power line based at least in part upon a determined time- varying temperature of a conductor in the power line, wherein the time-varying temperature is determined as a function of phasor measurements generated by one or more devices at vertices of the power line during the operation of the power line. ### Claim 17 (depends on 16) The apparatus of claim 16, further comprising a temperature calculator that determines the temperature of the conductor based at least in part upon the phasor measurements. ### Claim 18 (depends on 16) The apparatus of claim 16, wherein the sag calculator computes a sag for a Ruling Span. ### Claim 19 (depends on 18) The apparatus of claim 18, wherein the sag calculator computes the sag for the span as a function of the sag for the Ruling Span. ### Claim 20 (depends on 16) The apparatus of claim 16, further comprising a logger that logs a plurality of sags computed by the sag calculator over time. ### Claim 21 (depends on 20) The apparatus of claim 20, further comprising a trender that discerns trends in data logged by the logger. ### Claim 22 (depends on 16) The apparatus of claim 16, further comprising a notifier that transmits a notification to an operator, wherein the notification is based at least in part upon the sag computed by the sag calculator. ### Claim 23 (depends on 16) The apparatus of claim 16, wherein the sag calculator iteratively computes a tension of the conductor line of the span and a length of the conductor at the determined temperature until the computed tension and the computed length converge, and further wherein the length is employed to determine the sag for the span. ### Claim 24 A computer-readable medium comprising computer-executable instructions for: calculating, in real time during the operation of a power line, the time-varying sag for a span of the power line based at least in part upon a time varying temperature of conductors in the line section, wherein the temperature is ascertained through analysis of phasor measurements obtained during the operation of the power line; and storing the calculated sag. ### Claim 25 (depends on 24) The computer-readable medium of claim 24 comprising further computer-executable instructions for: computing an ohmic resistance of the conductors based at least in part upon phasor measurements generated by phasor measurement units; and determining the temperature of the conductors based at least in part upon the computed ohmic resistance. ### Claim 26 (depends on 24) The computer-readable medium of claim 24 comprising further computer-executable instructions for calculating the sag for the span based at least in part upon a length of a conductor of the span at a known reference temperature. ### Claim 27 (depends on 24) The computer-readable medium of claim 24 comprising further computer-executable instructions for calculating the sag for the span based at least in part upon a tension of a conductor of the span at a known reference temperature. ### Claim 28 (depends on 24) The computer-readable medium of claim 24 wherein the sag calculation does not account for a tension of the power line.