Modelagem e Ensaios do transformador de potência

Introduction to Power Transformer

In this section, the speaker introduces the concept of a power transformer and explains its ideal model.

Ideal Transformer Model

• An ideal transformer consists of a primary winding with N1 turns and a secondary winding with N2 turns.

• When a sinusoidal alternating voltage (v1) is applied to the primary winding, it induces a voltage (V2) in the secondary winding.

• The fundamental equation of a transformer states that the ratio between the primary and secondary voltages is proportional to the ratio of their respective number of turns.

Real Transformer Model

This section discusses the real model of a transformer, which includes losses and other components.

Losses in Real Transformers

• In practice, transformers have losses due to resistance in windings (R1 and R2), known as Joule losses.

• There are also dispersion reactances caused by magnetic flux dispersion. These represent magnetic flux that does not circulate through the core but disperses outside.

Magnetic Core Representation

• The real model includes a parallel excitation branch representing the magnetic core.

• This branch consists of two elements:

• A resistance representing heating losses in the core due to eddy currents and hysteresis.

• A magnetizing reactance representing the magnetism required for proper transformer operation.

Importance of Parameters and Testing

This section emphasizes the importance of determining parameters through testing for power flow analysis, short-circuit analysis, parallel operation, and efficiency calculations.

Parameter Determination

• To analyze power flow, short circuits, parallel operation, and efficiency calculations accurately, various tests need to be conducted on power transformers.

• Two common tests are:

• No-load test (vazio): Determines parameters of the excitation branch (core losses and magnetizing reactance).

• Short-circuit test (curto-circuito): Determines equivalent winding resistance and impedance.

No-Load Test

This section explains the procedure for conducting a no-load test on a power transformer.

Setup

• Instruments required: ammeter, voltmeter, and wattmeter.

• The secondary side of the transformer is left open while applying the rated voltage to the primary side.

Simplified Model

• Since no current flows through the secondary winding, resistance and dispersion reactance can be neglected.

• The wattmeter measures power loss in the core directly. Resistance RC can be calculated by dividing the square of voltage by active power.

Current Calculation

• Primary current is equal to voltage divided by resistance RC.

• Magnetizing current is determined by subtracting the square of primary current from previously calculated RC-based current.

Summary of No-Load Test

This section summarizes the calculations performed during the no-load test.

Parameters Determined

• The no-load test allows us to determine two important parameters:

• Resistance (RC) representing core losses.

• Reactance of magnetization, obtained by dividing voltage by magnetizing current.

Short-Circuit Test

This section explains how to conduct a short-circuit test on a power transformer.

Setup

• Similar instruments are used as in the no-load test.

• The secondary side is short-circuited while gradually increasing voltage on the primary side until reaching nominal current.

Simplified Model

• Magnetizing branch can be neglected due to low currents involved.

• Equivalent winding resistance (R) is calculated by dividing power by the square of current.

• Equivalent impedance is obtained by dividing voltage by current.

Summary of Short-Circuit Test

This section summarizes the calculations performed during the short-circuit test.

Parameters Determined

• The short-circuit test allows us to determine two important parameters:

• Equivalent winding resistance (R).

• Equivalent impedance, obtained by dividing voltage by current.

These tests and parameter determinations are crucial for accurate analysis and operation of power transformers.

Understanding Transformer Testing

In this section, the focus is on transformer testing and the importance of resistance and reactance in transformer modeling. The short-circuit test is discussed as a means to determine the equivalent resistance and reactance.

Short-Circuit Test for Equivalent Resistance and Reactance

• The practical aspects of transformers are mainly concerned with the equivalent resistance and reactance.

• The short-circuit test helps determine these parameters.

• The mathematical model used for transformers is typically a single-phase model.

Three-Phase Transformer Testing

This section introduces three-phase transformer testing, specifically focusing on the open-circuit test in a three-phase transformer setup.

Open-Circuit Test in Three-Phase Transformers

• In a three-phase transformer, the open-circuit test is conducted with no load connected.

• Instruments are installed at both high voltage and low voltage sides to measure current and power.

• The average of the calculated currents from ammeters gives the active power per phase.

Calculation of Current and Active Power

This section explains how to calculate current and active power using readings from instruments during the open-circuit test.

Calculation of Current and Active Power

• The average of calculated currents from ammeters provides the effective current per phase.

• Active power per phase can be obtained by summing up wattmeter readings divided by three.

Modeling Three-Phase Transformers

This section discusses how to use previous formulas for single-phase models to calculate resistance and magnetizing reactance in three-phase transformers.

Utilizing Single-Phase Model Formulas

• Previous formulas used for single-phase models can be applied to calculate resistance and magnetizing reactance.

• Instruments are installed at high voltage for short-circuit testing, while low voltage terminals are short-circuited.

Short-Circuit Test in Three-Phase Transformers

This section explains the process of conducting a short-circuit test in three-phase transformers and how to calculate equivalent parameters.

Calculation of Current and Power

• The current and power per phase can be calculated using formulas from the previous single-phase model.

• By applying these formulas, the equivalent resistance and reactance can be determined.

Calculation of Transformer Parameters

This section provides an example problem where all transformer parameters need to be calculated based on given test results.

Example Problem

• A 100 kVA single-phase transformer with primary voltage of 1000 V and secondary voltage of 100 V is considered.

• Test results include open-circuit test readings (100 V, 6 A, 400 W) and short-circuit test readings (50 V, 100 A, 1800 W).

• The task is to calculate all transformer parameters and draw the equivalent circuit referred to the high-voltage side.

Calculation of Resistance in Open-Circuit Test

This section focuses on calculating resistance based on open-circuit test data.

Resistance Calculation

• Resistance representing core losses can be obtained by dividing the square of voltage by power.

• In this case, a resistance value of 25 ohms is obtained when referred to the low-voltage side.

Calculation of Magnetizing Current

This section explains how to calculate magnetizing current based on open-circuit test data.

Magnetizing Current Calculation

• Magnetizing current can be calculated by dividing voltage by resistance.

• In this case, a magnetizing current of 4.47 A is obtained.

Calculation of Magnetizing Reactance

This section discusses the calculation of magnetizing reactance based on open-circuit test data.

Magnetizing Reactance Calculation

• Magnetizing reactance can be calculated by dividing voltage by magnetizing current.

• In this case, a magnetizing reactance value of 22.4 ohms is obtained when referred to the low-voltage side.

Reflection of Impedances to High-Voltage Side

This section explains how to reflect impedances from the low-voltage side to the high-voltage side using the transformer turns ratio.

Impedance Reflection

• Impedances need to be reflected from the low-voltage side to the high-voltage side using the transformer turns ratio.

• The turns ratio in this example is 10, resulting in reflected impedances of 2500 ohms for resistance and 2240 ohms for reactance on the high-voltage side.

Calculation of Equivalent Resistance in Short-Circuit Test

This section focuses on calculating equivalent resistance based on short-circuit test data.

Equivalent Resistance Calculation

• Equivalent resistance can be calculated by dividing power reading by the square of current.

• In this case, an equivalent resistance value of 0.18 ohms is obtained when referred to the high-voltage side.

Calculation of Equivalent Reactance in Short-Circuit Test

This section explains how to calculate equivalent reactance based on short-circuit test data.

Equivalent Reactance Calculation

• Equivalent reactance can be calculated by dividing voltage by current.

• In this case, an equivalent reactance value of 0.467 ohms is obtained when referred to the high-voltage side.

Circuit Equivalent and Conclusion

This section concludes the discussion by summarizing the circuit equivalent and parameters obtained from the tests.

Circuit Equivalent and Parameters

• The circuit equivalent can be drawn based on the calculated resistance and reactance values referred to the high-voltage side.

• The parameters obtained include resistance, reactance, and turns ratio for both open-circuit and short-circuit tests.