# Projects:2014S1-29 Measurement and Estimation of Transformer Parameters

## Contents

**Project Information**

**Aim**

The aim of this project is to rigorously combine measurements of practical transformers, with standard transformer-models, using the method of least squares and optimisation techniques, to obtain best estimates of transformer-model parameters. Transformers are the most important building-block of power transmission systems. They are used to transform the magnitudes of voltages and currents. They are used to match sources to loads, to reduce losses, and to improve efficiency. They isolate consumers from dangerous voltages in the transmission network. One of the main problems with modelling transformers is that the fields are distributed in space, which means that lumped models will always be approximate. Also, most practical transformers are significantly non-linear due to saturation of magnetic materials. Transformer models are always provisional, and only apply within certain ranges of current, and frequency. The practical goal of a modeller is to match a chosen equivalent-circuit, to a given device in such a way as to minimise any discrepancy between the observed behaviour of the device and the predicted behaviour of the model.

**Outline of Main Tasks**

- Task 1: Literature search on transformer models and measurement techniques
- Task 2: Identification of a suitable physical transformer for initial study
- Task 3: Open-circuit tests of the transformer using inductor models
- Task 4: Open-Circuit and Short-circuit tests of the transformer, using inductor, and coupled-magnetic-circuit models.
- Task 5: Full-analysis of the transformer, under many (at least seven...) loading conditions, and full estimates of all parameters.

**High Level Design**

- Stage 1:
- Basic equipment setup(transformer, current sensor)

- Stage 2:
- SC & OC tests based on the transformer module, transformer parameter estimation

- Stage 3:
- Analysis and error correction of estimated parameters.

**Experimentation **

Throughout the course of the project three main experiments were conducted. The aim of these experiment sessions was to acquire measurement values for four variables represented in the ideal transformer equivalent: The voltage across the primary terminal, V_{1}, the current flowing through the primary terminal, i_{1}, the voltage across the secondary terminal, V_{2} and the current flowing through the secondary terminal, i_{2}. Consequently these variables would be used to estimate the parameters represented in the ideal transformer equivalent circuit which can be written in terms of transmission parameters.

**Calibration Test**

The calibration test was conducted to obtain a relationship between the output voltage signal of the hall-effect current sensors used and the corresponding current flowing through them. This was implemented through a series circuit implementation, consisting of a constant DC voltage source, mulimeter, current sensor and a known resistive load. The current through the circuit was measured using the multimeter along with the corresponding output voltage signal from the sensor. Multiple readings were take and a plot obtained showing the linear relationship between the current and output voltage signal.

**Open Circuit Test**

The open circuit test was conducted in order to obtain necessary data to estimate the internal core resistance, R_{c} , and the magnetizing reactance, X_{M} of the transformer model. The transmission parameters estimated using these values are T_{11} and T_{21}.

**Short Circuit Test**

The short circuit test was conducted in order to obtain necessary data to estimate the total winding resistance R, and the total leakage reactance X of the transformer model. The transmission parameters estimated using these values are T_{12} and T_{22}.

**Analysis Procedure**

**Structure**

From the above experimentation following steps are undertaken when analyzing the data.

The obtained data are processed through a method named "Lease Square Spectral Analysis" to obtained phasors and then calibrated to get the transformer parameters. These calibrated data are then used to estimate the transformer parameters R_{c}, X_{m}, R_{1}, X_{1}, R'_{2}, X'_{2} and a (turns ratio). These estimations will then be use to calculate the T parameters T_{11}, T_{21}, T_{12} and T_{22}.

**Least Squares Spectral Analysis**

Lease Squares Method fit a set of data into a known function. This method is used in this project is to obtain phasors for V_{1}, I_{1}, V_{2} and I_{2} when 2500 samples of raw data are obtained from the experimentation.

u is found as a solution for the equation Ax = b where A is the matrix containing the measured data, x is the matrix containing the T parameters and b is the phasors obtained from the measured data. [1]

**Team**

**Group Members**

- Chandima De Silva
- David Minh Nguyen
- Rui Song

**Supervisors**

- Dr Andrew Allison
- Dr Rastko Zivanovic

**Workplace**

- Bench 6 in Project Lab

**Future Work**

The high voltage experiments can be undertaken so the non-linearity can also be taken into account when estimating the transformer parameters.

**References**

[1] Campbell, S.L., Meyer Jr., C.D. (1991). Generalized Inverses of Linear Transformations. 2nd ed. New York: Dover Publications, Inc.. p28-30.