Parameter estimation for and use of a thermal model of a power line

Abstract

A relationship between a temperature T<SUB>l </SUB>of a power line or power transmission conductor 10, an electrical quantity of the power line such as a current l or power flow P through the power line, as well as meteorological quantities or ambient conditions of the power line such as wind speed W, wind direction, humidity, solar radiation S and ambient temperature T<SUB>a</SUB>, is established in the form of a thermal model of the power line. Values of the aforementioned quantities or variables are continuously measured, and the collected values of the quantities are evaluated in order to update model parameters of the thermal model during operation of the power line. In an exemplary embodiment, an average temperature representative of the entire line is determined via two phasor measurement units (PMU) 11, 11' providing synchronized phasor values from two ends of the power line. An ohmic resistance of the power line can be computed from the phasor values, from which in turn the average line temperature can be derived.

1 . A method of estimating model parameters (A, B, . . . ; C l , . . . ) of a thermal model of a power line, comprising: 
 measuring values of an electrical quantity (l, P) of the power line and of meteorological quantities (T a , S, W) representing ambient conditions of the power line;    calculating values of the model parameters from said measured values;    measuring, repeatedly during operation of the power line, momentary values (l i , T a   i , S i , W i ) of the electrical and meteorological quantities;    measuring concurrently a momentary value (T l   i ) of a temperature (T l ) of the power line; and    calculating, repeatedly during operation of the power line, the values (A i , B i ; . . . ; C l   i , . . . ) of the model parameters from said measured values.    
     
     
         2 . The method according to  claim 1 , wherein measuring a momentary value (T l   i ) of the temperature of the power line comprises: 
 measuring, by means of two Phasor Measurement Units, synchronized phasor data (v 1   i , i 1   i ; v 2   i , i 2   i ) at two ends of the power line;    computing a value (R l   i ) of an electrical resistance (R l ) of the power line from the phasor data; and    computing, from the value (R l   i ) of the electrical resistance of the power line, an average line temperature as the momentary value (T l   i ) of the temperature of the power line.    
     
     
         3 . The method according to  claim 2 , wherein computing the average line temperature involves an analytical expression with parameters (R 0 , α 0 ) suitably calibrated by means of an independent line temperature measuring device.  
     
     
         4 . The method according to  claim 1 , wherein measuring momentary values (T a   i , S i , W i ) of the meteorological quantities involves measuring the values by a provider of meteorological data other than an operator of the power line.  
     
     
         5 . The method according to  claim 1 , comprising: 
 generating a series of measured values (T l   1 , T l   2 , . . . ; u 1 , u 2 , . . . ) of the temperature of the power line and the electrical and meteorological quantities; and    adaptively calculating updated values (A k , B k ; . . . ; C l   k , . . . ) of said model parameters every time a new value (T l   k , u k ) of the temperature of the power line or the electrical and meteorological quantities is measured.    
     
     
         6 . The method according to  claim 1 , wherein the thermal model is a nonlinear parametric model based on a heat balance equation.  
     
     
         7 . A method for predicting a value (T l   f ) of the line temperature of the power line, using a thermal model with momentary model parameter values (A i , B i ; . . . ; C l   i , . . . ) estimated according to  claim 1 , comprising: 
 providing forecasted values (u f ) of the electrical and meteorological quantities; and    calculating a power line temperature forecast (T l   f ) based on the momentary model parameters and the forecasted values of the electrical and meteorological quantities.    
     
     
         8 . The method according to  claim 7 , comprising: 
 comparing the power line temperature forecast (T l   f ) with a power line temperature limit; and    calculating a maximum allowable value of the electrical quantity (l, P) there from.    
     
     
         9 . The use according to  claim 8 , comprising: 
 using a linear thermal model for the power line; and    providing the maximum allowable value of the electrical quantity (l, P) to a balance market clearing process.    
     
     
         10 . The method according to  claim 2 , comprising 
 generating a series of measured values (T l   1 , T l   2 , . . . ; u 1 , u 2 , . . . ) of the temperature of the power line and the electrical and meteorological quantities; and    adaptively calculating updated values (A k , B k ; . . . ; C l   k , . . . ) of said model parameters every time a new value (T l   k , u k ) of the temperature of the power line or the electrical and meteorological quantities is measured.    
     
     
         11 . A method for predicting a value (T l   f ) of the line temperature of the power line, using a thermal model with momentary model parameter values (A i , B i ; . . . ; C l   i , . . . ) estimated according to  claim 2 , comprising: 
 providing forecasted values (u f ) of the electrical and meteorological quantities; and    calculating a power line temperature forecast (T l   f ) based on the momentary model parameters and the forecasted values of the electrical and meteorological quantities.    
     
     
         12 . A method for predicting a value (T l   f ) of the line temperature of the power line, using a thermal model with momentary model parameter values (A i , B i ; . . . ; C l   i , . . . ) estimated according to  claim 3 , comprising: 
 providing forecasted values (u f ) of the electrical and meteorological quantities; and    calculating a power line temperature forecast (T l   f ) based on the momentary model parameters and the forecasted values of the electrical and meteorological quantities.    
     
     
         13 . A method for predicting a value (T l   f ) of the line temperature of the power line, using a thermal model with momentary model parameter values (A i , B i ; . . . ; C l   i , . . . ) estimated according to  claim 4 , comprising: 
 providing forecasted values (u f ) of the electrical and meteorological quantities; and    calculating a power line temperature forecast (T l   f ) based on the momentary model parameters and the forecasted values of the electrical and meteorological quantities.    
     
     
         14 . A method for predicting a value (T l   f ) of the line temperature of the power line, using a thermal model with momentary model parameter values (A i , B i ; . . . ; C l   i , . . . ) estimated according to  claim 5 , comprising: 
 providing forecasted values (u f ) of the electrical and meteorological quantities;    calculating a power line temperature forecast (T l   f ) based on the momentary model parameters and the forecasted values of the electrical and meteorological quantities.    
     
     
         15 . A method for predicting a value (T l   f ) of the line temperature of the power line, using a thermal model with momentary model parameter values (A i , B i ; . . . ; C l   i , . . . ) estimated according to  claim 6 , comprising: 
 providing forecasted values (u f ) of the electrical and meteorological quantities;    calculating a power line temperature forecast (T l   f ) based on the momentary model parameters and the forecasted values of the electrical and meteorological quantities.    
     
     
         16 . A method for predicting a value (T l   f ) of the line temperature of the power line, using a thermal model with momentary model parameter values (A i , B i ; . . . ; C l   i , . . . ) estimated according to  claim 10 , comprising: 
 providing forecasted values (u f ) of the electrical and meteorological quantities; and    calculating a power line temperature forecast (T l   f ) based on the momentary model parameters and the forecasted values of the electrical and meteorological quantities.    
     
     
         17 . A method of estimating a parameter of a thermal model of a power line, comprising: 
 measuring a value of an electrical quantity of the power line and at least one meteorological quantity representing an ambient condition of the power line;    calculating a value of the parameter of the thermal model from said electrical quantity and said meteorological quantity;    measuring, during operation of the power line, a momentary value of each the electrical quantity an the meteorological quantity;    measuring a momentary value of a temperature of the power line; and    calculating, during operation of the power line, a value of the parameter from said measured values of the electrical quantity, the meteorological quantity and the temperature.