Computing methods for defining power transmission lines equivalent circuit parameters based on phasor measurements 

Our experts designed and tested computing methods for defining power transmission lines equivalent circuit parameters of main network equipment components, such as power lines, converters, reactors, etc (basic network equipment). This technology significantly improves quality of calculations for electric modes of an energy system, which enables greater precision in assessing network equipment throughput capacity and a significant increase in its economic efficiency.


Power system control is based on employing its computational model the backbone of which is an equivalent circuit. The equivalent circuit element parameters are generally defined by the corresponding equipment reference data or datasheet. Although considered to be constant these parameters depend upon the element actual load, weather conditions and other factors. 

The errors of the equivalent circuit parameters defined that way are significant and may reach +16¸-20% for resistance R and exceed 100% for active conductivity G. Hence the problem of defining the valid equivalent circuit parameters is of crucial importance in terms of power system controllability, stability and reliability.


The stated problem may be solved by deriving the parameters from the two system states combined. The state measurements must include the currents and voltages at both ends of the line regarding the Π-shaped equivalent circuit. That said at present time the equivalent circuit parameters might be otherwise defined involving modern systems of phasor measurements (WAMS) on a real-time basis.


The method of defining the equivalent circuit parameters based on phasor measurements along with general relations between power system state parameters has been proposed by our specialists. The obvious advantage of the proposed method is its simplicity and the potential of online implementation.


Simulink module have been employed in order to validate the proposed approach. The method itself and the algorithm developed according to the concept proved to be effective.


It should be noted that while dealing with the actual PMU data obtained from power system the measurement errors influence the results quite substantially. It is of particular concern regarding the instrument transformers admissible errors, angular errors especially. At the same time the PMU contribution to measurement errors meeting the requirements of IEEE C37.118 standard is small to negligible.


The equivalent circuit parameters have been defined for the 500 kV transmission line of roughly 200 km length and 993 MW power flow. The results are shown in Table 1. There are expected values and standard deviations for the time span of 10 min.

Table 1. Defined equivalent circuit parameters

Consequently the proposed and developed method of defining the equivalent circuit parameters based on real-time phasor measurements are limited by the measurement errors of instrument transformers. Nevertheless according to the investigation X and B (reactive parameters, three phases included) might be defined with reasonable accuracy concerning practical application.