Simulation of magnetics for power electronics using Python

Explore the basics of magnetism in electrical circuits, linking flux, current, and inductors through Faraday's and Lenz's laws, and model magnetic fields via simulations.

Explore the basics of inductors, right-hand rule for magnetic fields, flux and flux linkage, inductance, and induced emf from changing current via Faraday's and Lenz's laws.

Explore the magnetomotive force of a coil as the driving force for the magnetic field, defined by ampere-turns and linked to flux through inductance and the magnetic circuit.

See how current drives magnetic flux in an inductor core. Learn how reluctance and permeability shape flux in magnetic circuits, comparing iron and air.

Model magnetic circuits by calculating reluctance of iron cores and air gaps, acknowledging fringing and flux leakage, and apply series and parallel combinations to predict flux in power electronics.

Learn the B-H equation, where flux density B equals the permeability μ times the magnetic field strength H, independent of core geometry.

Explore the B-H curve and its hysteresis, revealing how flux density, residual flux density, and coercivity govern magnetization and demagnetization in power electronics cores.

Learn to model an inductor with a mathematical input-output framework, using integral equations, flux linkages, and parasitic effects to simulate magnetic behavior in power electronics.

Install the circuit simulator by setting up a Python conda environment, installing dependencies from requirements, running Django migrations, and launching the web server to run the simulator.

Set up a simple R-L circuit in a circuit simulator, create a new simulation file, configure a voltage source, resistor, and inductor, and prepare output data for analysis.

Simulate an inductor from the library within the power electronics magnetics course. Adjust inductance and resistance to produce a 45 degree current and voltage lag and plot the results.

Create a custom inductor model for a magnetics simulation by exporting parameters, building a controlled source with a high resistance, and updating circuit schematics for quick reuse.

Build a custom inductor model in Python by solving the inductor equation with resistance, integrating over time, and validating against built-in models.

Explore numerical integration for magnetic circuit simulations, moving from backward Euler to a four-slope method using k1–k4, and examine how parasitic resistance and output impedance shape inductor behavior.

Simulate an inductor with a magnetic core, calculating flux linkage, flux density, and field strength, then implement magnetic model and prepare for an air gap analysis in the next lecture.

Simulate a magnetics-based inductor core with an air gap in python, examining flux, flux linkage, and reluctance to understand inductance and phase between current and voltage.

Apply basic physics laws to model inductors, compute flux and flux linkages, and simulate custom components, guiding transformers and multi-winding machines.

Explore the fundamentals of coupled inductors and transformer-like magnetics, building a mathematical model from Faraday's and Lenz's laws to simulate coils in the same core using Python.

Explore magnetic coupling: multiple coils on a shared core induce voltages through changing flux that links the coils, enabling energy transfer with electrical isolation.

Explore how energy transfers between magnetically coupled coils, requiring changing current and flux linkages, and how core material, coupling strength, and load affect power transfer.

Express coupling between coils by flux linkage equations: L1 i1 plus or minus M i2, and L2 i2 plus or minus M i1, with sign indicating aiding or opposing flux.

Explore how mutual inductance relates to self-inductance in a two-coil magnetic circuit, derive flux linkage expressions, and define the coupling factor to account for leakage.

Model the coupled inductors by representing the magnetic circuit and flux linkages. Solve the simultaneous equations to determine coil currents and adjust the controllable source to simulate the behavior.

Edit the coupled inductor schematic by duplicating the magnet circuit, importing files, renaming voltages and currents, and isolating the inductors on a separate model sheet, then verify the schematic.

Code the magnetic circuit of two coupled inductors in python, configuring inductors, parasitic resistances, meters, and a control voltage source, and implement the mutual coupling equations to run the simulation.

Analyze first results from a two-coil coupled inductor using simultaneous equations, and compare manual methods with matrix-based solutions for flux linkages and coil voltages in simulation.

Demonstrate a no-load simulation of magnetics in a python-based power electronics model, highlighting input power factor and magnetization current differences, and how impedance matching stabilizes simulations under light load.

Explore impedance matching in magnetically coupled coils under a high resistive load, and observe how a short circuit on the second coil causes voltage collapse and flux interactions.

Match the internal resistance of the inductor model to the network impedance to achieve impedance matching and preserve inductive dynamics, using a medium range value to balance accuracy and stability.

Explore how an R-L load connects to the output coil in a magnetics simulation, analyzing voltage, current lag, and reflected current due to coupling for impedance matching.

Explore impedance matching for the output coil with a r-l load by balancing the inductor's internal resistance and its inductive reactance.

Simulate coupled coils with different turns to see how voltage and current change, and how inductance scales with turns as flux links energy transfer between windings.

Explore how reversing winding sense of coils, from assisting to opposing, changes flux linkage, polarity, and induced DMF in coupled coils, using Python simulations to verify Faraday's and Lenz's laws.

Express equations for magnetics as a matrix form to solve for currents, using inductance matrices, state vectors, and differential equations, with substitution and solving triangular systems.

Convert a matrix to upper triangular form using matrix and row operations. Swap rows, create nonzero diagonal elements, and eliminate below the diagonal to simplify the equation.

Solve matrix equations in magnetics simulation using back substitution on upper triangular forms. Update inductance, parasitic resistance, and inductor currents in a Python-based iterative workflow.

Debug and run the matrix equation solver in magnetics power electronics simulation, fix undefined variables, and incrementally optimize with triangularization and updated matrices for faster, more accurate results.

Wraps up the section by tying together theory and simulation of magnetic coupling between inductors, exploring mutual inductance, energy transfer, and impedance matching in transformer-like networks.

Explore how coupled inductors on the same core transfer energy between coils, distinguish transformers designed for power transfer, and introduce transformer concepts, polarity, and simulations using Python.

Explore transformer basics: how coupled windings transfer energy via magnetic flux with minimal leakage, and how voltage and current ratings define safe operation.

Explore transformer winding inductances, including leakage, magnetizing, and mutual inductance, and learn to calculate magnetizing current and leakage from rated voltage and current between primary and secondary.

Explore how transformer winding turns ratios set voltage and current transfer between windings, and how impedance scales with the square of the turns ratio in power electronics simulations.

Learn to set up a transformer simulation: back up circuit files, configure data and export controls, and rename transformer windings and components for a clear, workable model.

Edit transformer circuit parameters to align windings and loads and fix label references. Verify schematic integrity and polarity to enable reliable magnetics simulation.

Configure transformer models by updating the descriptor and replacing inductor variables with winding variables, then align inputs and outputs in the control editor for accurate Python simulations.

Define transformer parameters and calculate self inductance, leakage inductance, magnetizing inductance, and mutual inductance from winding ratings and voltages, using Python to build a realistic power electronics simulation.

Verify control code and interpret simulation parameters in a Python-based magnetics model, balancing output resistance for stability and dynamic response, and debug using plots and prints.

Run a transformer simulation to plot winding voltage and current, and verify a one-to-one transformer. Analyze the primary magnetizing current and DC offset to understand leakage and losses.

Explore transformer inrush current dynamics in a Python-based magnetics simulation, focusing on the primary DC offset, its decay through parasitic resistances, and the resulting flux demagnetization.

Explore how a step-up transformer raises secondary voltage from the primary, analyzes turns ratio effects on inductance, current, and impedance, and links results to Faraday's law.

Explore how transformer current transformation follows Faraday's and Lenz's laws, with the primary magnetizing current adjusting to secondary induced emf and inverse turns ratio under varying loads.

Include the core loss component in the simulation model by adding a magnetic loss resistor across the winding to represent core losses, alongside the winding parasitic resistance to improve accuracy.

Explore dot polarities in transformer windings to see how winding sense affects flux and induced emf in simulations. Apply Faraday's and Lenz's laws to determine whether windings assist or oppose.

Explore simulating a transformer with opposing dot polarities by inverting the model instead of changing flux equations, and verify via input-output plots to understand dark polarity conventions.

Simulate a transformer with multiple windings. Create circuit schematics linking one primary to three secondary windings from a single source, exploring isolation of windings and flux linking per Faraday's law.

Edit circuit parameters for a multi winding transformer in a Python magnetics simulation, adjusting load patterns, reversing polarity, and updating voltage sources and resistances via the control file.

Edit the magnetic model of a four-winding transformer by extending the control inputs, updating input/output variables, resistances, and mutual inductances, and assembling a four-by-four coupling matrix for simulation.

Explore how to analyze multi-winding transformer simulations in Python, interpreting winding voltages, polarity, and current transformation to validate isolation and step-up/step-down behavior.

Conclude the section on magnetics simulation in power electronics with Python, detailing multi-winding transformers, dot polarities, flyback concepts, and a scalable matrix-based modeling approach.

Introduce magnetics simulation for power electronics using Python, focusing on a flyback converter’s transformer, high-frequency operation, multiple isolated outputs, and how to modify the simulation model for high-frequency transformers.

Explore how dc-dc power converters regulate input voltages, use buck and boost topologies, and achieve isolation with flyback transformers to deliver multiple isolated outputs at high frequency.

Explore the flyback converter topology: how energy stores in the magnetizing inductance during on-time and discharges through the secondary to charge the output, with multiple windings and a regulated output.

Explore high frequency transformers in flyback converters, driven by switching frequency rather than grid frequency. Higher frequency reduces flux requirements, enabling smaller ferrite-core transformers versus laminated iron at 50/60 Hz.

Design and simulate a flyback converter circuit in a Python-based magnetics framework, integrating input and interface circuits, transformer windings, switches, capacitors, and output load.

Edit the flyback converter parameters in a Python-based magnetics simulation, resolve schematic errors by adjusting dump labels and component values (DC source, switch, capacitor, ammeter), and export updated circuit models.

Explore implementing pulse width modulation to control a flyback converter switch, generating a duty-cycle PWM with a carrier wave and debugging the control logic.

Verify the switched voltage on the flyback transformer primary by analyzing pulse width modulation signals in a python-based magnetics simulation, noting duty cycle effects and leakage spikes.

Reverse the polarity of windings two and four on the flyback transformer to align dot polarities with the primary winding, ensuring correct magnetization and safe operation in flyback mode.

Code the parameters of a high-frequency transformer for a flyback converter in Python simulations, covering windings, inductance, leakage, mutual inductance, and voltage handling.

This lecture explains how to solve simulation instability in magnetics for power electronics using python by decreasing the integration time step, analyzing leakage inductance, diagonal matrix elements, and high-frequency effects.

Analyze transformer winding voltages in a flyback converter using Python simulations, comparing primary and secondary windings, and explaining induced DMF and polarity during on/off states, and duty cycle effects.

Observe the cycle-by-cycle charging and discharging of the output capacitor in a magnetics simulation, analyzing the primary and secondary currents and the resulting oscillatory behavior.

Analyze the transient waveforms of a flyback converter’s output by examining secondary winding oscillations, output capacitor voltage, and the charging current driven by magnetizing inductance in a Python-based simulation.

Conclude by examining high-frequency flyback transformer simulations in Python, showing how reducing the integration timestep improves stability and how frequency dictates transformer behavior, with comparisons of primary and secondary currents.

Learn how transformers and magnetics in power electronics rely on basic physics, using open-source simulations to model magnetic circuits, air gaps, and energy transfer with Faraday's and Lenz's laws.