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Step-down transformer

Introduction

This example demonstrates the operation of a step-down single-phase transformer.

Model description

The example model uses blocks from the fundamental section of the Engee library for physical modelling. The transformer is designed for power $50 Вт$, operating frequency $60 Гц$, $120 В$ input voltage and $12 В$ output voltage. The efficiency is assumed to be $94\%$, the no-load magnetising current is $1\%$ and the leakage reactance is $2,3\%$. Losses in the core are not considered. It is assumed that the dependence $B(H)$ of the core material is linear.

electric_transformer.png

Initially, the transformer operates in no-load mode. At the time $t=0.5 с$ the nominal load "load " is switched on. Due to winding resistance and dissipation inductance, the secondary voltage drops from $12 В$ to $11.3 В$. A current $3.9 А$ is formed on the secondary winding of the transformer.

Modelling

Let's load and execute the developed model.

In [ ]: 
Путь_примера = @(__DIR__);
Имя_модели = "electrical_transformer";
Путь_модели = joinpath(Путь_примера, Имя_модели*".engee")

if Имя_модели ∉ getfield.(engee.get_all_models(), :name)
    engee.load(Путь_модели);
end

модель = engee.run(Имя_модели);

Let's get the variables displayed in the model for further construction.

In [ ]: 
# Время
t = модель["V_1"].time;
# Напряжения
V_1 = модель["V_1"].value;
V_2 = модель["V_2"].value;
# Токи
I_1 = модель["I_1"].value;
I_2 = модель["I_2"].value;
# Магнитные потоки и мдс
Ф = модель["Ф"].value;
Ф2σ = модель["Фl_2"].value;
F = модель["МДС"].value;

Modelling results

Let us plot the graphs of electrical variables - voltages and currents of primary and secondary windings.

In [ ]: 
# Подключаем библиотеку Plots и бэкэнд
using Plots
plotlyjs()

plot(t, [V_1 V_2]; layout = (2,1), subplot = 1, ylabel = "Напряжение, В", label = ["V_1" "V_2"], title="Напряжения и токи")
plot!(t, [I_1 I_2]; subplot = 2, ylabel = "Ток, А", label = ["I_1" "I_2"], xlabel = "Время, c")
Out[0]:

As can be seen from the voltage and current graphs, the transformer reduces the voltage and increases the current. Once the rated load is connected to the secondary winding circuit, the rated currents begin to flow through the windings.

Let us plot the magnetic variables - the main magnetic flux $Ф$, the leakage magnetic flux through the secondary winding $Ф_{2\sigma}$ and the magnetomotive force (MMF).

In [ ]: 
plot(t, Ф.*1e3; layout = (3,1), subplot = 1, ylabel = "Поток, мВб", label = "Ф", title="Магнитные переменные")
plot!(t, Ф2σ.*1e6; subplot = 2, ylabel = "Поток, мкВб", label = "Ф2σ", color=:green)
plot!(t, F; subplot = 3, ylabel = "мдс, А⋅в", label = "мдс", color=:red, xlabel = "Время, c")
Out[0]:

As can be seen from the graphs, the main magnetic flux after the secondary load is connected to the transformer decreases by the values of the leakage magnetic fluxes, and the magnetomotive force is formed in the magnetic core.

Conclusion

In this case study, a model of a 220/12 V step-down transformer operating at rated load has been considered. The dynamics of the electrical and magnetic variables of the system have been considered.

Blocks used in example