【Practical Exercise】Simulink Detailed Simulation of a Small Wind Power Generation System

# 1. Introduction to Simulink

Simulink is a graphical simulation platform developed by MathWorks, widely used in modeling, simulation, and analysis of control systems, signal processing, and dynamic systems. It offers an intuitive user interface that allows users to create models by dragging and dropping modules, and analyzes system behavior through simulation. Simulink integrates a rich library of modeling, including various physical, mathematical, and control system modules, enabling users to quickly build complex system models.

# 2. Modeling a Small Wind Power System

### 2.1 Wind Turbine Model

#### 2.1.1 Wind Turbine Power Curve

The wind turbine power curve describes the output power of a wind turbine at different wind speeds. It is typically represented by a piecewise linear function:

P(v) = {
    0, v < v_ci
    P_ri(v - v_ci) / (v_ri - v_ci), v_ci <= v < v_ri
    P_ri, v_ri <= v < v_co
    P_co(v - v_co) / (v_fo - v_co), v_co <= v < v_fo
    0, v >= v_fo
}

Where:

- `P(v)` is the wind turbine output power.
- `v` is the wind speed.
- `v_ci` is the cut-in wind speed.
- `v_ri` is the rated wind speed.
- `P_ri` is the rated power.
- `v_co` is the cut-out wind speed.
- `v_fo` is the free-stream wind speed.

#### 2.1.2 Wind Turbine Torque Equation

The wind turbine torque equation describes the output torque of the wind turbine at different wind speeds. It typically takes the following form:

T(v) = {
    0, v < v_ci
    T_ri(v - v_ci) / (v_ri - v_ci), v_ci <= v < v_ri
    T_ri, v_ri <= v < v_co
    0, v >= v_co
}

Where:

- `T(v)` is the wind turbine output torque.
- `v` is the wind speed.
- `v_ci` is the cut-in wind speed.
- `v_ri` is the rated wind speed.
- `T_ri` is the rated torque.
- `v_co` is the cut-out wind speed.

### 2.2 Generator Model

#### 2.2.1 Generator Equivalent Circuit

The generator equivalent circuit usually adopts a three-phase winding model, including stator winding, rotor winding, and magnetic circuit. In the equivalent circuit, the stator winding is represented by resistance `R_s` and inductance `L_s`, the rotor winding is represented by resistance `R_r` and inductance `L_r`, and the magnetic circuit is represented by mutual inductance `M`.

#### 2.2.2 Generator Power Equation

The generator power equation describes the output power of the generator under different speed and load conditions. It typically takes the following form:

P_g = 3 * V_s * I_s * cos(φ)

Where:

- `P_g` is the generator output power.
- `V_s` is the stator winding voltage.
- `I_s` is the stator winding current.
- `φ` is the power factor.

### 2.3 Transmission System Model

#### 2.3.1 Gear Ratio

The gear ratio describes the relationship between the wind turbine speed and the generator speed. It is usually determined by the gear ratio of the gearbox.

#### 2.3.2 Gearbox Efficiency

Gearbox efficiency describes the energy loss during the transmission of power. It usually takes the following form:

η_g = P_out / P_in

Where:

- `η_g` is the gearbox efficiency.
- `P_out` is the gearbox output power.
- `P_in` is the gearbox input power.

# 3. Simulink Simulation Platform

### 3.1 Setting Up Simulation Environment

#### 3.1.1 Installing Simulink Software

1. Go to MathWorks official website to download Simulink software.
2. Follow the prompts to complete the installation process.
3. Open Simulink software after installation.

#### 3.1.2 Creating and Editing Models

1. Click "New" in the Simulink interface to create a new model.
2. Browse and select the required modules in the "Library Browser."
3. Drag and drop the modules into the model workspace.
4. Connect the modules with lines to form the model structure.

### 3.2 Setting Simulation Parameters

#### 3.2.1 Simulation Time Step

The simulation time step is the interval at which the model state is calculated during the simulation. A smaller step size can improve simulation accuracy, but it will increase the simulation time.

**Code Block:**

sim_step_size = 0.01;   % Simulation time step (seconds)

**Parameter Explanation:**

* `sim_step_size`: Simulation time step in seconds.

**Logical Analysis:**

This code sets the simulation time step to 0.01 seconds. A smaller step size can capture more subtle changes in the model, but it will increase the simulation time.

#### 3.2.2 Simulation Termination Condition

The simulation termination condition specifies when the simulation should stop. It can be set to run for a certain amount of time, reach specific conditions, or manually stopped by the user.

**Code Block:**

sim_stop_time = 10;   % Simulation termination time (seconds)

**Parameter Explanation:**

* `sim_stop_time`: Simulation termination time in seconds.

**Logical Analysis:**

This code sets the simulation termination time to 10 seconds. The simulation will automatically stop when the simulation time reaches 10 seconds.

### 3.3 Analyzing Simulation Results

#### 3.3.1 Visualizing Simulation Data

After the simulation is completed, the simulation data can be visualized to analyze and evaluate the model performance.

**Code Block:**

figure;
plot(t, y);
xlabel('Time (s)');
ylabel('Signal Value');
title('Simulation Results');

**Parameter Explanation:**

* `t`: Simulation time data.
* `y`: Simulation output data.

**Logic