The problem
Inverter reliability is limited mainly by thermal cycling of the power modules, which fatigues bond wires and solder layers. Designers need junction temperature over realistic drive cycles, not just at a steady operating point, but full switching simulations of a whole drive cycle are far too slow. Combining tabulated losses with thermal networks solves this and supports both cooling design and lifetime estimation.
Objectives
- Build a loss model from datasheet conduction and switching data with temperature dependence.
- Fit Foster thermal networks from datasheet transient thermal impedance curves.
- Couple losses and temperatures in a closed electro-thermal loop.
- Validate the fast averaged model against a detailed switching model.
- Predict junction temperature cycling and a lifetime indicator over drive cycles.
What you need
Tools and toolboxes
- Simulink — Averaged loss model, thermal network integration and drive-cycle runs.
- Simscape Electrical — Semiconductor blocks with thermal ports and tabulated losses for the detailed reference model; Foster and Cauer thermal model blocks.
- Simscape — Thermal domain elements for heatsink and coolant (installed with Simscape Electrical).
- Curve Fitting Toolbox — Optional: fitting Foster network parameters to Zth curves. lsqcurvefit from Optimization Toolbox, or a hand-written least-squares fit, also works.
Software
- MATLAB R2023b or later
- Simulink
- Simscape Electrical
- WLTP and MIDC speed–time data
- A vehicle and motor model from an earlier project
Extra parts and data
- Datasheet of an automotive IGBT or SiC MOSFET module — Conduction, switching energy and transient thermal impedance curves are needed to make the loss and thermal model credible.
Key concepts
- Tabulated losses
- Conduction voltage and switching energies are stored as tables against current, voltage and junction temperature, interpolated at each operating point.
- Foster and Cauer networks
- Foster networks are fitted directly from Zth curves but have no physical node meaning; Cauer networks represent physical layers and can be connected to heatsink models.
- Electro-thermal coupling
- Losses depend on junction temperature and temperature depends on losses, so the two must be solved together.
- Thermal cycling lifetime
- Lifetime models relate cycles to failure to temperature swing and mean temperature; rainflow counting turns a temperature history into a set of cycles.
Step-by-step guide
- 1
Define the inverter and cycle
Choose labelled example values: a 400 V, roughly 100 kW car inverter with six-pack IGBT or SiC modules, 10 kHz switching, liquid cooling at a stated coolant temperature. Pick the drive cycles (WLTP Class 3 and MIDC) and use an existing vehicle and motor model to convert them into motor current, voltage, power factor and fundamental frequency over time. Keep the vehicle model fixed for all later runs.
Checkpoint: Time series of phase current RMS, modulation index, power factor and frequency over both cycles.
- 2
Build the loss tables
Digitise from the datasheet the on-state voltage versus current at two temperatures and the switching energies Eon, Eoff and Erec versus current at the test voltage and two temperatures. Store them as tables, scale switching energy linearly with DC-link voltage and interpolate in temperature. Plot the tables and check them against the datasheet figures. Note the gate resistance at which switching energy was measured.
Checkpoint: Interpolated tables reproduce the datasheet curves at both temperatures.
- 3
Fit thermal networks
Digitise the junction-to-case transient thermal impedance Zth(t) for the switch and diode and fit a four-term Foster network Zth(t) = Σ Ri·(1 − exp(−t/τi)) by least squares. Add case-to-heatsink and heatsink-to-coolant resistances with example values. Convert to a Cauer form if you need to couple to a physical heatsink model. Also note the cooling assumptions behind the case-to-heatsink value, since this term often dominates and can change results more than the device itself.
Checkpoint: Fitted Zth curves match the datasheet within a few per cent over the full time range.
- 4
Build the detailed reference model
Build one inverter phase leg with Simscape Electrical semiconductor blocks with thermal ports, parameterised with the loss tables and thermal networks, driven by sinusoidal PWM into an RL load. Run a few fundamental periods at a handful of operating points and log losses and junction temperatures. This is the reference for the fast model. Use a fine fixed step, for example 20 ns, and halve it once.
Checkpoint: Losses and junction temperatures at reference points are logged and physically sensible.
- 5
Build the averaged loss model
Build a fast model that, at each time step, computes average switch and diode losses over a fundamental period from the analytical sinusoidal-PWM expressions using current, modulation index, power factor, DC-link voltage and junction temperature. Optionally compute instantaneous losses within the fundamental period at low frequencies, where temperature ripple at the fundamental matters. Record the speed-up factor of the averaged model compared with the detailed one.
Checkpoint: Averaged losses agree with the detailed reference model within a stated margin at every reference point.
- 6
Close the electro-thermal loop
Feed losses into the thermal networks and junction temperature back into the loss tables. Integrate with a variable-step solver and check that results do not change when the maximum step is halved. Run a steady operating point and confirm the converged temperature against a hand calculation of P·Rth. Include a transient check as well: apply a step in loss and compare the junction temperature rise with the fitted Zth curve, which confirms the network is implemented correctly.
Checkpoint: Steady-state junction temperature matches P·Rth within a few per cent.
- 7
Run the drive cycles
Run WLTP and MIDC and log junction temperature for the switch and diode in one leg. Find peak junction temperature and the largest swings, and check the special case of hill start or stall, where low fundamental frequency concentrates losses in one device. Script all runs with sim(). Present results for switch and diode separately, because during regeneration the diodes carry more of the loss and may become the limiting devices.
Checkpoint: Junction temperature traces for both cycles and the stall case with peaks and swings identified.
- 8
Estimate lifetime indicators
Apply rainflow counting (for example the rainflow function in Signal Processing Toolbox, or your own implementation) to junction temperature histories to obtain cycle counts by swing and mean temperature. Apply a published power-cycling lifetime model with clearly cited parameters to estimate damage per cycle and compare cycles and conditions. Present results as relative damage between cycles and conditions, since the absolute lifetime depends strongly on lifetime model parameters that carry large uncertainty.
Checkpoint: A table of damage per cycle for WLTP, MIDC and stall, with the dominant cycle ranges identified.
- 9
Sensitivity and design study
Vary coolant temperature, switching frequency and thermal interface resistance, and compare Si IGBT with SiC MOSFET data if available. Report how peak temperature and damage change. Identify the design lever with most effect. Change one parameter at a time from the baseline, keep the drive cycle fixed, and present the results as a tornado chart. This shows clearly which design choice gives the largest reduction in peak temperature and damage, and helps decide where engineering effort is best spent.
Checkpoint: Sensitivity plots of peak temperature and damage against each parameter.
- 10
Research write-up
Document the loss tables, thermal fits, validation against the detailed model, drive-cycle results, lifetime method and sensitivity. State clearly that lifetime numbers are relative indicators that depend on the chosen model and parameters. Release scripts and digitised data where allowed. Compare predicted temperatures with any published measurements for similar modules, and state clearly what the model adds, such as fast drive-cycle prediction with validated accuracy.
Checkpoint: A thesis chapter draft with reproducible validation and clearly caveated lifetime results.
Testing & validation
- Loss tables reproduce datasheet curves.
- Foster fit matches datasheet Zth.
- Averaged model agrees with detailed switching model.
- Steady-state temperature matches P·Rth.
- Drive-cycle temperature histories and rainflow-based damage computed.
Expected results
A validated fast electro-thermal inverter model that predicts junction temperatures over full drive cycles, with a comparison of cycles and design parameters on relative lifetime damage.
Research angle for your M.Tech thesis
Research questions: how accurately can an averaged electro-thermal model predict drive-cycle junction temperature compared with detailed switching simulation, and which operating conditions dominate thermal-cycling damage for Indian urban cycles versus WLTP? Metrics: temperature prediction error, simulation speed-up, peak temperature, damage per cycle. Baselines: steady-state thermal design and detailed switching simulation. Lifetime model parameters must be cited and their uncertainty discussed. A validated fast model with a cycle-level comparison including MIDC conditions and a sensitivity study is the kind of contribution suitable for a conference paper.
Take it further
- Couple a coolant loop model and study pump control strategies.
- Add active thermal control by varying switching frequency.
- Include bond-wire degradation feedback on on-state voltage.
- Compare different module packages from datasheets.
Viva and review questions
Why not run a switching model over the whole drive cycle?
Switching events at 10 kHz need nanosecond to microsecond steps, which makes a 30-minute cycle impractically slow; an averaged loss model validated against the switching model gives the same thermal answer much faster.
Why are Foster networks fine for the device but Cauer used for heatsink coupling?
Foster parameters fit the measured curve but their nodes are not physical, so connecting another thermal stage to them is incorrect; Cauer networks keep physical meaning at their nodes.
Why is a stall or hill start a severe case?
At very low fundamental frequency one device carries peak current for a long time, so its junction temperature follows the current and can rise much higher than the average suggests.
Learn it at DIYguru
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