Inductive Wireless Charging: Coil Coupling and Resonant Compensation

The problem

Wireless charging removes the cable and suits automated parking and bus depots, but power transfer depends strongly on how well the two coils are aligned and how the resonant circuits are tuned. Without compensation, the large leakage inductance makes the link impractical. This project models the link and quantifies the effect of misalignment and tuning on power and efficiency.

Objectives

• Model two coupled coils with self-inductances, mutual inductance and resistances.
• Design series–series compensation capacitors for a chosen resonant frequency.
• Build a full-bridge inverter, the coupled link, a rectifier and a battery load.
• Measure power transfer and efficiency against coupling coefficient and frequency.
• Explain frequency splitting at strong coupling.

What you need

Key concepts

Coupling coefficient

k = M/√(L1·L2) measures how much of one coil's magnetic flux links the other. For EV pads it is typically low, often between about 0.1 and 0.3, and falls with gap and misalignment.

Series–series compensation

A capacitor in series with each coil cancels its self-inductance at the resonant frequency, f0 = 1/(2π√(L·C)). This lets real power pass through a link that would otherwise be dominated by reactive current.

Frequency splitting

Above a critical coupling the single resonant peak of the link splits into two, and the maximum power no longer occurs at f0. It matters when a vehicle is very closely aligned.

Reflected impedance

The secondary circuit appears in the primary as an impedance (ωM)²/Z2. At resonance this is purely resistive, which is why compensation gives efficient power transfer.

Step-by-step guide

1. 1

   Set the design targets

   Choose an example: 3.3 kW output into a 350 V battery, an 85 kHz operating frequency (a commonly used band for vehicle wireless charging), a nominal coupling of 0.2 and a coil gap of about 150 mm. Pick example coil values, such as L1 = L2 = 120 µH with an AC resistance of 0.1 Ω each. Write a parameter script that computes M = k·√(L1·L2) and the compensation capacitors.

   Checkpoint: Capacitor values computed so that both tanks resonate at 85 kHz within 0.5 per cent.

2. 2

   Build the analytical model

   In MATLAB, write the two-loop equations at the fundamental frequency: V1 = (jωL1 + 1/(jωC1) + R1)·I1 − jωM·I2 and 0 = −jωM·I1 + (jωL2 + 1/(jωC2) + R2 + Rac)·I2, where Rac = 8·RL/π² is the equivalent AC resistance of the rectifier and battery. Solve for currents, output power and efficiency over a frequency sweep from 60 to 110 kHz for k from 0.1 to 0.4.

   Checkpoint: Plots of power against frequency showing a single peak at low k and two peaks at high k (frequency splitting).

3. 3

   Model the coupled coils

   In Simscape Electrical place a Mutual Inductance block (or two linked inductors with a coupling parameter) with L1, L2 and M, and add series resistors for winding loss. Add the compensation capacitors. Drive the primary with an ideal sinusoidal source at 85 kHz and load the secondary with Rac. Use a variable-step stiff solver or a discrete step of about 50 ns. Compare currents with the analytical model.

   Checkpoint: Simulated primary and secondary current amplitudes agree with the analytical model within about 3 per cent.

4. 4

   Add the inverter and rectifier

   Replace the sine source with a full-bridge MOSFET inverter on a 400 V DC bus, driven by square-wave gating at 50 per cent duty with a small dead time. Replace the load resistor with a diode bridge, an output filter capacitor and a battery modelled as a voltage source with series resistance. Set the solver step small enough for clean switching edges, for example 20 ns.

   Checkpoint: Output DC power settles near 3.3 kW at k = 0.2, and the inverter current is close to sinusoidal because the tank filters harmonics.

5. 5

   Check soft switching

   Plot inverter output voltage and current together. At exact resonance the current is in phase with voltage; slightly above resonance it lags, which allows zero-voltage switching of the MOSFETs. Shift the switching frequency by 1–3 kHz above f0 and observe the phase. Record the trade-off between soft switching margin and reduced power transfer. Measure the phase angle between voltage and current at each frequency offset and note the switch current at turn-off, since a positive current at turn-off allows the MOSFET output capacitance to discharge before the next turn-on.

   Checkpoint: Waveform plots showing current lagging voltage when the frequency is set slightly above resonance.

6. 6

   Sweep coupling and misalignment

   Model misalignment as a reduction in k, using an example curve where k falls from 0.25 at perfect alignment to 0.1 at 150 mm lateral offset. Run sim() for each k value with Simulink.SimulationInput, logging output power, input power and coil currents. Compute DC-to-DC efficiency as output over input power. Note that in a series–series link, output power can rise as k falls at fixed input voltage.

   Checkpoint: A plot of power and efficiency against k, with efficiency falling and coil currents rising at low coupling.

7. 7

   Add simple power control

   Add a PI controller that adjusts either the inverter phase-shift (between the two legs) or the DC bus voltage to hold output current at a setpoint as k changes. Phase-shift control is easy to implement with two PWM generators offset in time. Test the controller over the full misalignment range. Keep the controller bandwidth well below the switching frequency, for example a few hundred hertz, and sample it at a fixed rate so the PWM generators and the controller share a clean timebase.

   Checkpoint: Output current stays within a few per cent of its setpoint while k is ramped from 0.25 to 0.12.

8. 8

   Loss breakdown

   Calculate coil copper losses from I²·R, capacitor ESR losses if modelled, and estimate MOSFET conduction losses from on-resistance. Compare with total measured loss in the model. Present a loss breakdown at nominal and worst-case alignment, and discuss which component limits efficiency when the vehicle is badly parked. Use the RMS values of coil and switch currents over a whole number of switching periods, computed from logged signals in MATLAB, so the loss estimate is not biased by a partial cycle at the end of the run.

   Checkpoint: A loss breakdown whose sum matches input minus output power within a couple of per cent.

9. 9

   Report

   Present the design equations, analytical and simulated results side by side, the waveforms, the coupling sweep and the control test. State the limitations: lumped coil parameters with no magnetic field model, ideal switches apart from on-resistance, no electromagnetic field exposure analysis and no foreign-object detection. Explain how a finite-element coil model would feed better L and M values into the same Simulink link.

   Checkpoint: A report with analytical and simulated curves overlaid and all parameters stated.

Testing & validation

• Resonant frequency of each tank within 0.5 per cent of target.
• Simulation agrees with the analytical fundamental-frequency model.
• Frequency splitting visible at high coupling, as theory predicts.
• Loss breakdown sums to measured input minus output power.

Expected results

A switched Simulink model of a series–series compensated wireless charging link, verified against an analytical model, with power and efficiency curves against coupling and a working output-current controller.

Take it further

• Compare series–series with LCC–series compensation for misalignment tolerance.
• Model a coil pair in a finite-element tool and import L and M as functions of offset.
• Add secondary-side active rectification for bidirectional transfer.
• Study frequency tracking control to stay at the soft-switching point.

Viva and review questions

Learn it at DIYguru

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