Python for Power Electronics: Simulating Converters and Inverters

Power electronics is the backbone of modern electrical systems—from renewable energy systems and electric vehicles to industrial motor drives and consumer electronics. Central to power electronics are converters (DC-DC, AC-DC) and inverters (DC-AC), which modify voltage levels and waveforms to suit different applications.

While simulation tools like MATLAB/Simulink, PSIM, and LTspice are traditionally used for power electronics analysis, Python offers a powerful, flexible, and open-source alternative. With numerical libraries like NumPy, SciPy, and visualization tools like Matplotlib, engineers can simulate and analyze converters and inverters using Python.

This article provides a comprehensive, step-by-step guide to simulating power converters and inverters using Python, including theoretical background, mathematical modeling, time-domain simulation, and waveform analysis.

Introduction to Power Electronics

Power electronics involves the conversion and control of electrical energy using semiconductor switches (like MOSFETs, IGBTs) and passive components (inductors, capacitors, transformers). Typical conversions include:

DC-DC converters: Buck (step-down), Boost (step-up), Buck-Boost
AC-DC converters: Rectifiers
DC-AC converters: Inverters (single-phase, three-phase)

Key performance metrics:

Output voltage regulation
Ripple voltage
Switching frequency
Efficiency

Why Use Python for Simulation?

Python offers:

✅ Numerical Solvers for differential equations
✅ Customizable control algorithms
✅ Data visualization for waveform analysis
✅ Integration with machine learning, embedded systems
✅ Cost-effective and open-source

Python is ideal for educational purposes, R&D, or building custom tools.

Python Libraries for Power Electronics

Library	Purpose
`NumPy`	Vector/matrix computations, arrays
`SciPy`	ODE solvers, signal processing
`Matplotlib`	Time-domain waveform visualization
`SymPy`	Symbolic math (circuit modeling)
`Control`	Control system design and Bode plots

Modeling Power Electronic Devices

Power converters are modeled using switching differential equations. For example, a buck converter has two modes:

Switch ON: $V_L = V_{in} - V_o$ , $di_L/dt = V_L/L$
Switch OFF: $V_L = -V_o$ , $di_L/dt = V_L/L$

MOSFET and diode are modeled as ideal switches: ON = short, OFF = open.

DC-DC Converter Simulation: Buck Converter

Buck Converter Circuit Equations

Input voltage $V_{in}$ , Output voltage $V_o$
Inductor $L$ , Capacitor $C$ , Load resistance $R$
Switching frequency $f_{sw}$ , duty cycle $D$

State-space equations:

Let $x = [i_L, v_C]^T$

\frac{dx}{dt} = \begin{cases} \begin{bmatrix} 0 & -1/L \\ 1/C & -1/RC \end{bmatrix} x + \begin{bmatrix} 1/L \\ 0 \end{bmatrix} V_{in}, & \text{(Switch ON)} \\\\ \begin{bmatrix} 0 & -1/L \\ 1/C & -1/RC \end{bmatrix} x + \begin{bmatrix} 0 \\ 0 \end{bmatrix}, & \text{(Switch OFF)} \end{cases}

Python Simulation Example (Buck Converter)

import numpy as np
import matplotlib.pyplot as plt

Vin = 24     # Input voltage
L = 1e-3     # Inductance
C = 100e-6   # Capacitance
R = 10       # Load resistance
f_sw = 50e3  # Switching frequency
D = 0.5      # Duty cycle
T = 1 / f_sw
dt = T / 100

t = np.arange(0, 0.01, dt)
iL = np.zeros_like(t)
vC = np.zeros_like(t)

for k in range(1, len(t)):
    switch_on = (t[k] % T) < (D * T)
    if switch_on:
        vL = Vin - vC[k-1]
    else:
        vL = -vC[k-1]
    iL[k] = iL[k-1] + dt * (vL / L)
    vC[k] = vC[k-1] + dt * ((iL[k-1] - vC[k-1]/R) / C)

plt.figure(figsize=(10, 4))
plt.plot(t, vC, label='Capacitor Voltage (V_o)')
plt.plot(t, iL, label='Inductor Current (i_L)')
plt.xlabel('Time (s)')
plt.ylabel('Amplitude')
plt.title('Buck Converter Output')
plt.grid()
plt.legend()
plt.show()

DC-AC Inverter Simulation (Single-Phase Inverter)

Full-Bridge Inverter with Sinusoidal PWM

Converts DC to AC using four switches
SPWM (Sine PWM): Compares sine wave with high-frequency triangle

f_ac = 50
f_pwm = 10000
t = np.linspace(0, 0.1, 10000)

sine = np.sin(2 * np.pi * f_ac * t)
triangle = 1.2 * np.sign(np.sin(2 * np.pi * f_pwm * t))
pwm_signal = sine > triangle

plt.plot(t[:1000], sine[:1000], label="Reference Sine")
plt.plot(t[:1000], triangle[:1000], label="Carrier Triangle", alpha=0.5)
plt.plot(t[:1000], pwm_signal[:1000], label="PWM Output", linestyle='--')
plt.legend()
plt.title("SPWM Signal Generation")
plt.xlabel("Time (s)")
plt.grid(True)
plt.show()

Switching Control and PWM Implementation

PWM control in Python involves:

Reference waveform (sine, sawtooth, square)
Carrier waveform
Comparator logic to generate gate pulses

You can simulate PWM generation for converters, and apply to switching devices in time-domain simulation.

Time-Domain Simulation using Euler Method

Most simulations use the Euler or RK4 method to solve ODEs of power converters.

Euler method for a first-order system:

x(t+dt) = x(t) + dt \cdot \frac{dx}{dt}

Use this to update inductor current and capacitor voltage at each timestep.

Efficiency and Ripple Analysis

Efficiency $\eta$ :

\eta = \frac{P_{out}}{P_{in}} \times 100 = \frac{V_o^2 / R}{V_{in} \cdot I_{in}} \times 100

Ripple Voltage:

\Delta V = V_{max} - V_{min}

Can be extracted using np.max() and np.min() on capacitor voltage waveform.

Waveform Visualization

Use Matplotlib to plot:

Inductor current
Output voltage
PWM switching signal
Load current waveform
FFT for harmonic analysis

from scipy.fft import fft, fftfreq

N = len(vC)
yf = fft(vC)
xf = fftfreq(N, dt)[:N//2]

plt.plot(xf, 2/N * np.abs(yf[:N//2]))
plt.title("FFT of Output Voltage")
plt.xlabel("Frequency (Hz)")
plt.grid()
plt.show()

FAQs

Q1: Can Python simulate switching transients?

Yes, using small time steps (e.g., 1e-6s) and explicit numerical integration, Python can simulate switching dynamics.

Q2: What is the benefit of simulating in Python vs MATLAB?

Python is open-source, highly flexible, and integrates well with control logic, ML models, or web APIs.

Q3: How can I simulate EMI or harmonics?

Use FFT analysis (scipy.fft) to observe harmonic content in waveforms. For EMI, model parasitic elements like $L_{par}, C_{stray}$ .

Q4: Can Python interface with SPICE engines?

Yes, PySpice allows integration with NGSpice for circuit-level transient and AC simulations.

Q5: How accurate are Python simulations?

Python simulations using ODEs and ideal models are very accurate for educational, prototyping, and algorithm development purposes. For hardware-accurate simulations, use device-level models.

Conclusion

Python is a powerful tool for simulating and analyzing power electronic converters and inverters. With a combination of mathematical modeling, control logic, and waveform visualization, it offers an open-source alternative to proprietary tools for engineers, students, and researchers.

Whether you're simulating a buck converter, SPWM inverter, or building a custom digital controller, Python provides all the building blocks—from equations to execution.

Let me know if you'd like a downloadable Jupyter Notebook version, animated waveform plots, or want to extend this to three-phase inverter simulation or digital control implementation!

Prasun Barua