Degradation-Aware Energy Management for Hybrid Energy Storage

The problem

Most hybrid energy-storage strategies minimise energy loss or battery RMS current and assume that this also protects the battery. Battery ageing, however, depends non-linearly on current, temperature, SOC and depth of discharge, so the strategy that saves the most energy may not maximise battery life. Including a degradation model in the cost exposes this trade-off and the conditions under which it matters.

Objectives

• Implement a semi-empirical cycle and calendar ageing model with temperature dependence.
• Add a lumped battery thermal model to the hybrid storage simulation.
• Formulate a combined cost of energy loss and monetised capacity fade.
• Solve it by DP as a benchmark and with a real-time MPC or rule approximation.
• Quantify the Pareto trade-off between efficiency and projected battery life.

What you need

Key concepts

Semi-empirical ageing model

Capacity fade expressed as Q_loss = B·exp(−Ea / (R·T))·Ah^z, with parameters fitted to cycling data. It links throughput, temperature and current rate to fade without modelling the electrochemistry.

Calendar and cycle ageing

Calendar ageing happens with time, depending on SOC and temperature; cycle ageing depends on charge throughput and current. Both matter in daily vehicle use.

Monetised degradation cost

Capacity fade is converted to cost by dividing battery replacement cost by the fade allowed before end of life, so it can be added to an energy-loss cost with one weighting factor.

Efficiency–life Pareto front

The set of strategies where battery life cannot be extended without accepting more energy loss. Sweeping the weight traces it.

Step-by-step guide

1. 1

   Define scope and claims

   State the question: does including degradation in the cost change the optimal power split enough to matter, compared with minimising loss or RMS current? Choose the example system (48 V battery with supercapacitor bank for an L5 vehicle), the cycles and the metrics: energy loss per km, projected capacity fade per year of typical use, and battery temperature. Decide which claims the study can and cannot support with simulation alone.

   Checkpoint: A protocol with question, metrics, baselines and a list of claims out of scope.

2. 2

   Fit the ageing model

   From a public cycling dataset, extract capacity against throughput at different temperatures and C-rates. Fit the semi-empirical model with lsqcurvefit, then fit a calendar term against time and SOC if data exist. Hold back one test condition and check the prediction. Report parameter uncertainty from the fit's Jacobian. Plot fitted and measured capacity against throughput for every condition, and check that parameter values are physically sensible, for example a positive activation energy.

   Checkpoint: Predicted capacity fade on the held-out condition within a stated error of the measurement, with confidence intervals on parameters.

3. 3

   Add a thermal model

   Model the battery as a lumped thermal mass with heat generation I²R plus a reversible term if data allow, and convection to ambient through a thermal resistance: m·cp·dT/dt = Q_gen − (T − T_amb)/R_th. Use example values for a small pack and check the time constant is plausible. Feed temperature to the ageing model and to resistance via an Arrhenius factor.

   Checkpoint: Under a constant current step, temperature rises along a first-order curve with a time constant of tens of minutes for the example pack.

4. 4

   Integrate the storage model

   Combine battery (OCV, resistance, thermal, ageing), supercapacitor and averaged converter models in Simulink, driven by recorded load power from IDC, MIDC and WLTP. Log battery current, temperature, SOC and incremental fade. Check that fade accumulates sensibly over a cycle and scales correctly when the cycle is repeated. Check the energy balance of the combined model over one cycle and confirm that the thermal and ageing subsystems do not change the electrical results when their coupling is switched off.

   Checkpoint: Incremental fade per cycle is consistent when the same cycle is repeated, apart from the slow effect of temperature and SOC.

5. 5

   Define the cost and baselines

   Stage cost J = energy loss × energy price + w × fade × cost per unit fade. Baselines: loss-only strategy (w = 0), RMS-current minimisation, and a low-pass filter rule. Keep all prices and costs as clearly labelled example values and report results as relative changes so conclusions do not depend on one price assumption. Run each baseline once before optimisation and record its loss, fade and peak temperature, so later results can be expressed as changes from these references.

   Checkpoint: A cost definition with labelled example prices and three baseline strategies running in the model.

6. 6

   Solve the DP benchmark

   Solve DP with supercapacitor SOC as state; if battery temperature matters strongly, add it as a second state on a coarse grid and check the result against the 1-D version. Use the exact model's step equations. Repeat for a range of weights w. Verify grid convergence for the working resolution. Use the same model equations in DP as in the Simulink model, and note the run time for each weight, since adding a thermal state increases it greatly. Store the optimal trajectories for each weight.

   Checkpoint: DP solutions for at least five weights with grid-convergence evidence.

7. 7

   Draw the Pareto front

   For each weight, compute energy loss and fade per cycle, then project fade to a year of typical use with a repeated-cycle simulation that updates capacity and resistance. Plot fade against loss. Mark the baselines. The shape of the curve shows whether there is a free gain: lower fade at almost no loss, or a steep trade-off. Report the shape of the front around the baselines in words as well, since a reader needs to know whether the gain in life is large or small for a given loss penalty.

   Checkpoint: A Pareto plot with baselines marked and the projected battery life at each point.

8. 8

   Build a real-time controller

   Design an MPC with a short horizon of 5 to 10 s over predicted load from a simple predictor (constant or exponentially decaying). Linearise the ageing cost around the operating point, or use a quadratic current penalty weighted by a temperature-dependent factor that approximates it. Solve with quadprog each step or with the Model Predictive Control Toolbox. Respect converter and SOC limits.

   Checkpoint: The MPC runs each step well within the step time and keeps supercapacitor SOC within limits on all cycles.

9. 9

   Compare real-time against DP

   Run the MPC on all cycles at the weight selected from the Pareto front. Compute its gap to DP on the combined cost and its position on the fade–loss plot. Compare with the baselines. Report whether the degradation-aware MPC moves meaningfully towards the DP point or performs much like an RMS-current strategy. Also report MPC computation time per step and the number of steps where constraints were active, since a controller that only works with long horizons may not be implementable.

   Checkpoint: A table placing MPC, baselines and DP on both metrics for each cycle.

10. 10

    Sensitivity and uncertainty

    Propagate ageing-parameter uncertainty by sampling from the fitted confidence intervals and re-running the best and baseline strategies. Vary ambient temperature from 25 to 45 °C. Show whether the ranking of strategies holds under this uncertainty; if it does not, say so clearly. Use at least a few dozen parameter samples, report the fraction of samples in which the degradation-aware strategy still ranks best, and show the spread of projected fade for each strategy.

    Checkpoint: Ranking of strategies under sampled ageing parameters and three ambient temperatures.

11. 11

    Write up

    Present the ageing model with its fit and validation, thermal model, cost definition, DP Pareto front, MPC design and comparison, and the uncertainty study. State clearly that life projections come from a fitted model and simulation, not from cell tests. Release the fitted parameters and scripts. Include the ageing-model fit plots and the uncertainty results prominently, since the strength of every conclusion depends on them. Discuss what cell testing would be needed to confirm the life projections.

    Checkpoint: A thesis chapter or paper draft with an uncertainty-aware conclusion.

Testing & validation

• Ageing model predicts a held-out condition within stated error.
• Thermal model shows a plausible time constant and steady-state rise.
• DP grid convergence for each weight.
• MPC respects all limits and its gap to DP is reported.
• Strategy ranking tested under ageing-parameter uncertainty and ambient temperature.

Expected results

A degradation-aware energy-management study for hybrid storage: a fitted ageing model, an efficiency–life Pareto front from DP, a real-time MPC compared with loss-only and RMS baselines, and evidence on how robust the conclusions are to model uncertainty.

Take it further

• Replace the semi-empirical model with a reduced electrochemical ageing model.
• Add active cooling and include its energy in the cost.
• Validate ageing predictions on a small cell cycling rig.
• Extend to fuel-cell hybrids, adding stack degradation.

Viva and review questions

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