【Advanced】Introduction to the MATLAB_Simulink Power System Simulation Toolbox

# 1. Overview of MATLAB_Simulink Power System Simulation Toolbox

The MATLAB_Simulink Power System Simulation Toolbox is a powerful toolkit designed for modeling, simulating, and analyzing power systems. It offers a comprehensive library of power system components, including generators, transformers, transmission lines, and various simulation algorithms such as power flow analysis, short circuit analysis, and transient stability analysis. This toolbox is widely used in power system planning, design, operation, and control.

# 2. Fundamentals of Power System Modeling

Power system modeling is a critical step in power system analysis and simulation. This chapter will introduce modeling methods for common components in power systems and explore common methods for analyzing power systems.

### 2.1 Power System Component Modeling

Power systems consist of various components, including generators, transformers, and transmission lines. Accurate modeling of these components is vital for power system analysis and simulation.

#### 2.1.1 Generator Modeling

Generators are the main equipment for power generation in power systems. Generator models typically include synchronous generator models and asynchronous generator models.

**Synchronous Generator Model**

The synchronous generator model represents the generator as an ideal voltage source with internal impedance composed of armature resistance and inductance. This model is suitable for steady-state analysis, such as power flow analysis.

% Synchronous Generator Model Parameters
R_a = 0.01; % Armature Resistance
X_d = 0.2; % Direct-Axis Synchronous Reactance
X_q = 0.15; % Quadrature-Axis Synchronous Reactance
V_t = 1.0; % Terminal Voltage

% Synchronous Generator Model Equations
I_d = (V_t - E') / (R_a + j * X_d);
I_q = (V_t - E') / (R_a + j * X_q);

**Asynchronous Generator Model**

The asynchronous generator model represents the generator as an induction machine with a rotor speed that is not synchronized with the stator magnetic field. This model is suitable for transient stability analysis.

% Asynchronous Generator Model Parameters
R_s = 0.01; % Stator Resistance
X_s = 0.1; % Stator Inductance
R_r = 0.02; % Rotor Resistance
X_r = 0.15; % Rotor Inductance
s = 0.05; % Slip

% Asynchronous Generator Model Equations
I_s = (V_s - E') / (R_s + j * X_s);
I_r = (E' - s * V_s) / (R_r + j * X_r);

#### 2.1.2 Transformer Modeling

Transformers are devices used in power systems to change voltage levels. Transformer models typically include ideal transformer models and practical transformer models.

**Ideal Transformer Model**

The ideal transformer model represents the transformer as a lossless device, with primary and secondary voltages proportional to each other. This model is suitable for steady-state analysis.

% Ideal Transformer Model Parameters
n = 2; % Turns Ratio

% Ideal Transformer Model Equations
V_s = n * V_p;
I_p = I_s / n;

**Practical Transformer Model**

The practical transformer model considers transformer losses, including core losses and copper losses. This model is suitable for transient stability analysis.

% Practical Transformer Model Parameters
R_c = 0.01; % Core Resistance
X_m = 0.1; % Magnetizing Inductance
R_p = 0.02; % Primary Resistance
X_p = 0.15; % Primary Inductance
R_s = 0.03; % Secondary Resistance
X_s = 0.2; % Secondary Inductance

% Practical Transformer Model Equations
I_p = (V_p - E') / (R_p + j * X_p);
I_s = (V_s - E') / (R_s + j * X_s);

#### 2.1.3 Transmission Line Modeling

Transmission lines are devices used in power systems to transfer electrical energy. Transmission line models typically include distributed parameter models and lumped parameter models.

**Distributed Parameter Model**

The distributed parameter model represents the transmission line as a continuous distributed parameter system, taking into account the line's resistance, inductance, and capacitance. This model is suitable for transient stability analysis.

% Distributed Parameter Transmission Line Model Parameters
R = 0.1; % Resistance (Ohms/km)
L = 0.5; % Inductance (mH/km)
C = 0.01; % Capacitance (μF/km)
l = 100; % Line Length (km)

% Distributed Parameter Transmission Line Model Equations
V(x) = V_s * cosh((R + j * ω * L) * x / l);
I(x) = V_s * (sinh((R + j * ω * L) * x / l) / (R + j * ω * L));

**Lumped Parameter Model**

The lumped parameter model represents the transmission line as a concentrated network of resistance, inductance, and capacitance. This model is suitable for steady-state analysis.

% Lumped Parameter Transmission Line Model Parameters
R = 0.1 * l; % Resistance (Ohms)
L = 0.5 * l; % Inductance (mH)
C = 0.01 * l; % Capacitance (μF)

% Lumped Parameter Transmission Line Model Equations
V_r = V_s * (R + j * ω * L) / (R + j * ω * L + 1 / (j * ω * C));
I_s = V_s / (R + j * ω * L + 1 / (j * ω * C));

### 2.2 Power System Analysis Methods

Power system analysis is a key step in power system planning, operation, and control. Power system analysis methods include power flow analysis, short circuit analysis, and transient stability analysis.

#### 2.2.1 Power Flow Analysis

Power flow analysis determines the steady-state operating conditions of power systems. It considers the power system's topology, component parameters, and load demands, calculating the system's voltage, current, and power flow.

% Power Flow Analysis Steps
1. Initialize the power system model
2. Calculate node voltages
3. Calculate line currents
4. Check power balance
5. Repeat steps 2-4 until convergence

% Power Flow Analysis Results
Node voltages
Line currents
Power flow

#### 2.2.2 Short Circuit Analysis

Short circuit analysis determines how the power system responds when a short circuit fault occurs. It considers the power system's topology, component parameters, and fault type, calculating fault currents, voltage drops, and protective equipment operation times.