The problem
Urban driving puts sharp current pulses on an EV battery during acceleration and regeneration. High peak and RMS currents raise heating and are linked to faster ageing. A supercapacitor has low energy but very high power capability, so pairing it with the battery can shave the peaks, but only if the control strategy and supercapacitor size are chosen sensibly.
Objectives
- Model a battery, a supercapacitor bank and a bidirectional DC–DC converter on a common DC bus.
- Design a rule-based power split using a low-pass filter and supercapacitor SOC limits.
- Drive the system with a load profile from a vehicle model on IDC.
- Compare peak and RMS battery current with a battery-only system.
- Study the effect of supercapacitor size and filter time constant.
What you need
Tools and toolboxes
- Simulink — Vehicle load profile, energy management logic and the system test harness.
- Simscape Electrical — Battery, supercapacitor, averaged DC–DC converter and DC bus circuit; an averaged-model version can be built in base Simulink equations instead.
- Stateflow (optional) — Mode logic for supercapacitor SOC limits; Simulink Switch blocks are an alternative.
- MATLAB — Parameter scripts, sizing sweeps and metrics.
Software
- MATLAB R2023b or later
- Simulink
- Simscape Electrical
- CSV drive-cycle data (IDC)
Extra parts and data
None beyond the software above.
Key concepts
- Semi-active topology
- The battery connects directly to the DC bus and the supercapacitor connects through a bidirectional converter, which controls the supercapacitor's current independently of its voltage.
- Frequency-based power split
- A low-pass filter on load power gives the slow part to the battery; the remainder, the fast peaks, goes to the supercapacitor.
- Supercapacitor usable energy
- Energy is ½·C·V², so discharging from full voltage to half voltage uses 75 per cent of the stored energy. Operation below half voltage gives little energy at high current.
- Battery RMS current
- The root-mean-square current over a cycle, which sets I²R heating in the battery and is a common proxy for stress.
Step-by-step guide
- 1
Define the example system
Pick example values: a 48 V, 40 Ah lithium-ion battery for an L5 three-wheeler, a supercapacitor bank of 58 F at a 32 V maximum, and a 3 kW bidirectional converter. Derive the load from a vehicle model on IDC with peak power of about 4 kW. Set supercapacitor limits at 50 and 100 per cent of rated voltage. Write all values to a parameter script.
Checkpoint: A parameter script and a sizing check showing the supercapacitor stores enough energy for one acceleration of the example vehicle.
- 2
Generate the load power profile
Use a simple longitudinal model in Simulink to convert IDC speed into DC bus power, with motoring and regeneration efficiencies. Log it and save it as a timeseries. Running the storage model from a recorded profile keeps simulations fast and makes comparisons fair, because every variant sees exactly the same load. Check the profile's energy over one cycle against the consumption figure from the vehicle model, and note the largest power step, since it sets the converter's required rating.
Checkpoint: A load power plot with positive peaks during accelerations and negative regions during braking, and a cycle-average power that is a fraction of the peak.
- 3
Model the battery and supercapacitor
In Simscape Electrical, use the Battery block (or a Controlled Voltage Source with an OCV lookup and series resistance) for the battery and the Supercapacitor block for the bank, with its equivalent series resistance from a datasheet. Connect them to the DC bus through a Current Sensor and a Voltage Sensor. Use a Solver Configuration block and a local solver or the ode23t variable-step solver.
Checkpoint: Discharging each element alone at constant current gives a voltage curve of the expected shape: flat-ish for the battery, linear for the supercapacitor.
- 4
Model the converter at average level
Represent the bidirectional converter as an average model: a Controlled Current Source on the bus side whose current equals the supercapacitor-side power times efficiency divided by bus voltage. Command the supercapacitor current directly, with a current limit and a first-order lag of a few milliseconds standing in for the converter's current loop. An average model is enough for energy studies and runs far faster than switching.
Checkpoint: A power-balance check: bus-side power equals supercapacitor-side power times efficiency within 0.5 per cent.
- 5
Build the battery-only baseline
Remove the supercapacitor branch and let the battery supply the full load through the bus. Run the IDC profile and log battery current, voltage and SOC. Compute peak current, RMS current and the I²R loss in the battery's internal resistance. These numbers are the reference against which the hybrid is judged. Also log battery terminal voltage sag at the largest peak, since a hybrid that reduces sag gives the motor drive a steadier bus, a second benefit worth reporting.
Checkpoint: Battery-only peak and RMS current values recorded in a results table.
- 6
Design the rule-based split
Pass load power through a Transfer Fcn low-pass filter 1/(τs + 1) with τ around 10 s; this is the battery's share. The supercapacitor reference is the remainder. Add rules: if supercapacitor SOC is low, block discharge and recharge it slowly from the battery; if it is high, block charging and send regeneration to the battery. Add a small SOC restoring term so the bank returns to a target voltage.
Checkpoint: In a test with a step in load power, battery power rises smoothly with the chosen time constant while the supercapacitor covers the step.
- 7
Integrate and verify
Connect the split logic to the converter model and run the IDC profile. Check in the Simulation Data Inspector that supercapacitor voltage stays within limits, that the converter current limit is respected and that battery current is smoother than in the baseline. Also check energy conservation across the cycle by summing energy into and out of each element and the losses.
Checkpoint: Supercapacitor voltage stays between its limits for the whole cycle and the energy balance closes within 1 per cent.
- 8
Compare with the baseline
Compute battery peak current, RMS current, I²R loss and total system loss (battery, supercapacitor and converter) for the hybrid. Present them alongside the baseline. Point out that the hybrid adds converter loss, so total efficiency can fall even while battery stress drops; that trade-off is the honest result. Plot battery current for both systems on the same axes over a representative 200 s window, so the peak shaving is visible as well as summarised in the table.
Checkpoint: A comparison table showing lower battery peak and RMS current for the hybrid, with converter losses listed.
- 9
Sweep size and time constant
Script runs over supercapacitor capacitance (half, nominal and double) and filter time constants of 2, 5, 10 and 20 s using Simulink.SimulationInput arrays. Record battery RMS current and the fraction of time the supercapacitor sits at a limit. Plot RMS current against capacitance for each time constant to show diminishing returns. Use the same IDC profile for every run, and store each run's metrics in a table so the plots and the report draw on one consistent dataset.
Checkpoint: A sweep plot that shows where adding capacitance stops reducing battery RMS current noticeably.
- 10
Report
Document the topology, models, control rules, verification, baseline comparison and sweeps. State the limitations: average converter model, no thermal or ageing model, a single drive cycle and an energy-based supercapacitor model. Recommend a time constant and size for the example vehicle, giving the reason. This is a simulation-only project; building a high-current hybrid pack needs proper protection and supervision. Attach the parameter script and the sweep script so every result in the report can be reproduced in one run.
Checkpoint: A report with a recommendation supported by the comparison table and sweep plot.
Testing & validation
- Single-element constant-current tests give correct voltage behaviour.
- Converter average model conserves power within the stated efficiency.
- Supercapacitor voltage stays within limits on the full cycle.
- System energy balance closes within 1 per cent.
- Battery peak and RMS current compared with the battery-only baseline.
Expected results
A semi-active battery–supercapacitor hybrid model with rule-based control, showing quantified reductions in battery peak and RMS current on IDC, the converter loss it costs, and a sizing and tuning recommendation.
Take it further
- Replace the average converter model with a switched model and design its current loop.
- Add a battery thermal model and compare temperature rise.
- Compare with an optimisation-based split from dynamic programming.
- Try a fully active topology with two converters.
Viva and review questions
Why put the supercapacitor behind the converter rather than the battery?
Supercapacitor voltage swings widely as it charges and discharges, so the converter is needed to use most of its energy while the battery holds the bus voltage roughly steady.
What does the low-pass filter time constant control?
It sets how much of the load's fast content goes to the supercapacitor; a longer time constant smooths battery current more but needs a larger bank to avoid hitting its limits.
Why might total system efficiency fall in the hybrid?
Energy passing through the supercapacitor also passes through the converter twice, so converter losses can outweigh the reduction in battery I²R loss.
Learn it at DIYguru
These DIYguru courses and programmes teach what this project needs.