The impact of new energy generation grid-connected on grid power

Simulation Engine Components

Python Simulation Script

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp

def system_frequency_response(t, y, H, D, Pg, Pd_step, T_gov):
    """
    Single-Area Power System Frequency Response (SFR) Model
    y = [frequency_deviation (Hz), mechanical_power_deviation (p.u.)]
    """
    delta_f, delta_Pm = y
    
    # Trigger load step disturbance at t = 1.0s
    delta_Pd = Pd_step if t >= 1.0 else 0.0
    
    # Differential Equations
    ddelta_f_dt = (delta_Pm - delta_Pd - D * delta_f) / (2.0 * H)
    ddelta_Pm_dt = (-delta_Pm - (Pg * delta_f)) / T_gov
    
    return [ddelta_f_dt, ddelta_Pm_dt]

# --- Parameters & Conditions ---
f0 = 50.0            # Nominal grid frequency (Hz)
Pd_step = 0.05       # 5% load step disturbance at t=1s
D = 1.0              # Load damping factor (p.u./Hz)
Pg = 20.0            # Governor gain (1/R where R=0.05)
T_gov = 0.5          # Governor time constant (s)
t_span = (0, 10)     # Time domain (s)
t_eval = np.linspace(0, 10, 1000)

# Renewable Penetration Scenarios mapped to system inertia H (seconds)
scenarios = {
    "Low Renewable (High Inertia, H=6.0s)": 6.0,
    "Medium Renewable (Med Inertia, H=3.5s)": 3.5,
    "High Renewable (Low Inertia, H=1.5s)": 1.5
}

# --- Simulation Execution & Visualization ---
plt.figure(figsize=(10, 5.5), dpi=100)

for label, H_val in scenarios.items():
    sol = solve_ivp(
        system_frequency_response, 
        t_span, 
        [0.0, 0.0], 
        args=(H_val, D, Pg, Pd_step, T_gov),
        t_eval=t_eval
    )
    actual_freq = f0 + sol.y[0]
    plt.plot(sol.t, actual_freq, label=label, linewidth=2)

plt.axvline(x=1.0, color='#64748b', linestyle='--', label='Load Step (t=1.0s)')
plt.axhline(y=f0, color='#334155', linestyle=':', alpha=0.7)
plt.title('Impact of Renewable Integration on Grid Frequency Stability', fontsize=12, fontweight='bold')
plt.xlabel('Time (s)', fontsize=11)
plt.ylabel('Grid Frequency (Hz)', fontsize=11)
plt.grid(True, linestyle='--', alpha=0.5)
plt.legend(loc='lower right', fontsize=9.5)
plt.tight_layout()
plt.show()

Dynamic Variable Reference