تجزیه و تحلیل حساسیت مقادیر خطا

In this paper, a method for the sensitivity analysis of sequence fault currents and voltages in an unloaded overhead transmission line for perturbation in line parameters is described. The sensitivity of these quantities with respect to conductor radius, spacing between conductors, earth resistivity, height of conductor and frequency are evaluated for an overhead transmission line. The sensitivity predicts the effect of each parameter on fault currents and voltages, which help in tap setting of the relays for protecting the transmission line against faults. To demonstrate the potential of the proposed scheme, the sensitivity of fault currents and voltages for a three phase, 220 kV line has been studied and the results are presented.

Faults on an overhead transmission line can never be ruled out in-spite of the best transmission system design. Symmetrical components method is commonly employed for computing the currents, voltages and power during fault condition. Here, the unbalanced currents and voltages are resolved into symmetrical components viz positive, negative and zero sequence components. These fault quantities are computed and predicted based on the fixed line parameters such as conductor size, configuration of line, frequency and earth resistivity. Accordingly, the relay settings are made for isolating the faulty transmission line to keep the system stable. The sequence voltages and currents depend upon the impedance of the line, which can be derived from self and mutual impedance of transmission line. During a fault, the capacitance and the inductance of the transmission line change due to charging and discharging of electromagnetic and electrostatic circuits. Also, the line parameters such as radius of the conductor, height, spacing between conductors, frequency and resistivity may vary considerably along the line due to manufacturing defects, stringing, fault current etc. Thus, for a transmission line with known sending end voltage, it is of considerable interest to evaluate the sensitivity of fault quantities with respect to different line parameters. The motivation for this study has arisen from the working experience of authors related to malfunctioning of protective relays [1] and [2]. In this paper, the authors have carried out sensitivity analysis of fault current and voltage considering a 220 kV transmission line for perturbations in frequency, resistivity of earth, height, radius of conductor and spacing between conductors. The results of this study should be of interest to protection engineers and transmission system design engineers.

A mathematical model for evaluating the normalised sensitivity of sequence current and voltage during fault conditions of an unloaded transmission line was developed in this paper. This paper was used to study the effect of line parameters on fault currents and voltages respectively for different type of faults. The sequence currents are most sensitive to frequency, whereas voltages are insensitive to frequency. The sensitivity of sequence current and voltages for open conductor situations are negligible. Resistivity does not effects sequence currents and voltages. The result of our study should be of interest to engineers responsible for operation and protection of transmission system. The sensitivity of fault during transients can be computed by taking into account the effect of corona and exponential decay by computing the sensitivity function as discussed in Section 3. The authors have also developed a mathematical model for a loaded transmission line, which shall be communicated in the near future.