Achieving Better Accuracy in Modeling Voltage Transformers

Abstract

Transformers designed for operation at network frequencies (50 or 60 Hz) unavoidably transform also the voltages of higher harmonic components with frequencies up to 2 kHz. In modelling a voltage transformer (VT), a standard T-equivalent circuit with constant parameters at all frequencies is commonly used. This circuit contains a horizontal branch and a vertical branch. The horizontal branch parameters were taken equal for the primary and secondary windings. For an ideal VT, the horizontal branch resistances and inductances are equal to zero, and the vertical branch resistance and inductance are equal to infinity. The article analyzes the transformation ratio equal to the ratio of the effective voltage across the VT secondary winding to the effective voltage across its primary winding. The transformation ratio of an ideal VT is equal to the ratio of the numbers of turns in its secondary and primary windings. The transformation ratio error depends on the extent to which the VT parameters differ from the ideal values mentioned before. The necessary VT transformation accuracy depends on its application. Experimental investigations were carried out on a multipurpose Type OSM-1.0 UZ voltage transformer. Its parameters were determined in the frequency band from 50 Hz to 2 kHz according to the three voltmeter method using a 34401A voltmeter. To improve the modeling adequacy, the same parameters were determined by a Type E7-22 RLC meter at the frequencies equal to 120 and 1000 Hz. For both methods, the uncertainty of the VT parameter measurements and the actual discrepancy between the measured values obtained by both these methods were within 2%. To obtain generalized results, a normalized transformation ratio was introduced, the value of which for the ideal VT is equal to unity. The measured VT parameters were used to study the VT errors, as well as the errors of their assessments by means of three models: (i) the conventional one (involving four constant values of the parameters measured at the 50 Hz frequency), (ii) the reference one (involving the VT parameter values measured at all analyzed frequencies), and (iii) the new one (involving nine parameters measured at DC and at the 50 and 2000 Hz frequencies). The transformation ratio was calculated for all these models using the MicroCap and Wofram Mathematics computer programs in the no-load operation mode, during operation with the nominal active load of 50 Ω, and during operation with the nominal active load connected in parallel with a 10 µF capacitor. The frequency errors of the first and third models were determined with respect to the reference model and the 50 Hz frequency. It has been demonstrated from the simulation results that the proposed model yields the accuracy a factor of 1.5 to 3.6 better than the standard one.