How to establish equivalent circuit of transformer

In the field of electrical engineering, transformer is an important equipment to realize power transmission and voltage conversion. In order to analyze the operation characteristics and performance parameters of transformer, it is an essential tool to establish its equivalent circuit. Equivalent circuit can simplify the complex electromagnetic relationship into a circuit model which is convenient for calculation and analysis, thus helping engineers to better understand the working state of transformer.

# 1, the basic principle of transformer

Transformer works on the principle of electromagnetic induction, which consists of two or more windings wound on the same iron core. When the primary winding is connected with AC power supply, alternating magnetic flux will be generated in the iron core, and then electromotive force will be induced in the secondary winding. By changing the turns ratio of the winding, the voltage can be increased or decreased.

# 2. Basic structure of equivalent circuit

For the convenience of analysis, the electrical characteristics of transformer are usually equivalent to a circuit model including resistance, reactance and excitation branch. There are two common equivalent circuits: T-type equivalent circuit and γ-type (or approximate) equivalent circuit.

1. T type equivalent circuit
T-type equivalent circuit includes primary winding resistance of $ R_1 $ and leakage reactance of $ X_{σ1} $,secondary winding converted to primary side resistance of $ R'_2 $ and leakage reactance of $ X'_{σ2} $,and parallel excitation branch reflecting core loss, including excitation resistance of $ R_m $ and excitation reactance of $ x _ m. This model considers all electrical parameters and is suitable for accurate analysis.

2. Type γ equivalent circuit
In practical engineering, because the excitation current is relatively small, the excitation branch is often moved to the power supply end to form a γ-type equivalent circuit. This model simplifies the calculation process and is often used in the analysis of transformer load operation.

# 3, the steps of establishing equivalent circuit

1. Parameter conversion: In order to analyze the primary and secondary side parameters uniformly, the secondary side parameters are usually converted to the primary side. The conversion basis is the transformation ratio $ k = frac{N_1}{N_2} $,where $ N_1 $ and $ N_2 $ are the turns of the primary and secondary windings respectively.

2. Determination of circuit components: According to the experimental data or nameplate parameters, determine the resistance and reactance values. The primary winding resistance $ R_1 $ is obtained by no-load experiment, and the leakage reactance $ X_{σ} $ is calculated by short-circuit experiment.

3. Treatment of excitation branch: the excitation branch is composed of $ R_m $ and $ X_m $,which reflects the characteristics of iron loss and main flux. No-load experiment can be used to calculate the parameters of excitation branch.

4. Drawing equivalent circuit diagram: Draw the circuit diagram of all parameters according to T-type or γ-type connection mode, and mark the values of each component.

# IV. Application and Significance

The equivalent circuit can be used not only to calculate important parameters such as transformer efficiency, voltage regulation rate and short-circuit current, but also to design transformer protection system and optimize operation strategy. In power system analysis, the equivalent circuits of multiple transformers can also be connected in series or in parallel to form a more complex network for overall analysis.

To sum up, the establishment of transformer equivalent circuit is the key means to understand its working principle and carry out engineering analysis. Through reasonable model simplification and accurate parameter acquisition, the performance of transformer can be effectively evaluated and theoretical support can be provided for the stable operation of power system.