How to calculate the transient response of transformer

In power system, transformer is the key equipment to realize voltage conversion and energy transmission. When the system is disturbed by short circuit, lightning strike and switching operation, the transformer will experience transient process. Transient response not only affects the stability of the system, but also may cause damage to the transformer itself. Therefore, accurate calculation of transformer transient response is of great significance for equipment protection and safe operation of the system.

First, the basic concept of transformer transient response

The transient process of transformer usually occurs when the voltage or current suddenly changes, such as closing, opening and short circuit fault. At this time, the magnetic flux in the iron core and the current in the winding can't change suddenly, which leads to the free component current in the winding and forms a transient response. The response includes the process of establishing magnetic flux and the process of current transition, which has nonlinear and time-varying characteristics.

Second, the main influencing factors of transient response

1. Initial magnetic flux: The remanence in the iron core has a significant influence on the transient current during closing.
2. Closing angle: The phase angle of AC voltage determines the change rate of magnetic flux at the moment of closing, thus affecting the magnitude of inrush current.
3. Saturation characteristics of iron core: With the increase of magnetic flux density, the iron core enters saturation state, which leads to the decrease of inductance and the rapid increase of current.
4. Load state: The inrush current generated during no-load closing is much greater than that during on-load closing.

Three, the calculation method of transformer transient response

# 1. Analytical calculation based on magnetic circuit method

Transformer can be simplified as a coupled inductance system with nonlinear magnetic circuit. According to Faraday's law of electromagnetic induction and Ampere's law of loop, the magnetic circuit equation can be listed:

$$
frac{dPhi}{dt} = V - R i
$$

Where $Phi$ is magnetic flux, $V$ is voltage, $R$ is winding resistance and $i$ is current. Considering the nonlinear magnetization characteristics of iron core, the relationship between magnetic flux and excitation current is usually described by magnetization curve (B-H curve).

# 2. Numerical simulation method

Because analytical methods are difficult to deal with complex nonlinear and coupling problems, numerical simulation is often used to realize transient response analysis in engineering. Commonly used simulation tools include EMTP (Electro Magnetic Transients Program), PSCAD, MATLAB/Simulink, etc.

In simulation, transformers usually adopt the following model:

T-type equivalent circuit model: suitable for steady-state analysis;
-Detailed distributed parameter model: considering the distributed capacitance and inductance between windings, it is suitable for high frequency transient analysis;
Non-linear model of iron core: describe the B-H curve by look-up table or non-linear function, and simulate the characteristics of iron core by combining with hysteresis model.

# 3. Calculation of magnetizing inrush current

When the transformer is switched on with no load, a large transient excitation current is generated because the magnetic flux in the iron core can't suddenly change, which is called inrush current. Its peak value can reach 6~8 times of rated current, and its duration varies from tens of milliseconds to hundreds of milliseconds.

The calculation of inrush current can be based on the following steps:
-Suppose the initial magnetic flux of the iron core is $ phi _ 0 $;
-Calculate instantaneous voltage according to closing phase angle;
-Solving the magnetic field current by differential equation;
-introduce hysteresis and saturation characteristics for correction.

Four, engineering application and matters needing attention

In practical engineering, transformer transient response analysis is mainly used for:
-Design protection devices (such as differential protection against misoperation);
-Evaluate the capacity of circuit breakers;
-analyze the closing strategy to reduce the influence of inrush current;
-Study the influence of transient overvoltage on insulation.

In order to improve the calculation accuracy, the actual equipment parameters and operating conditions should be combined to model; At the same time, the influence of temperature, frequency and hysteresis on the core characteristics is considered.

V. Conclusion

The transient response of transformer is a comprehensive problem involving electromagnetism, magnetic circuit, material characteristics and system operation. By combining analytical method with numerical simulation, its transient behavior can be predicted accurately. With the development of power electronics and smart grid, the demand for rapid and accurate analysis of transient process is increasing day by day. In the future, it will rely more on high-precision modeling and real-time simulation technology to ensure the safe and stable operation of power system.