Energy Storage and EV Charging

The pack voltages:

A 40% voltage swing from empty to full — wider than the PV string's temperature range in Set 37, and every converter connected to the pack must work across all of it. That range is the single most demanding specification a battery converter faces.

The capacity:

Which for a 96-series pack means each cell is 211 Ah — achieved either with large-format cells or by paralleling many small ones. The choice affects the balancing problem, the thermal design and the failure modes, but not the electrical interface.

The fast-charge current:

Two C — the whole pack's energy delivered in half an hour. Four hundred amps is what makes charging cables heavy and, above about 200 A, liquid-cooled. It also makes every milliohm in the path matter: 1 mΩ of contact resistance dissipates 179 W.

The CC–CV profile:

The split explains the familiar charging curve. The first 80% arrives at full power; the last 20% takes as long again as the current tapers away. That is why manufacturers quote "10 to 80%" times — not marketing, but the physics of the CV phase.

Why the voltage must be held rather than the current. The cell voltage limit is a chemical boundary:

Exceeding it does not merely reduce life — it deposits metallic lithium on the anode, which is both a permanent capacity loss and a route to an internal short. The CV phase exists because the cell's terminal voltage includes its internal \(IR\) drop, so holding a safe terminal voltage while the current falls lets the true cell potential approach the limit asymptotically.

Cell balancing. Series cells are never identical:

A 2% spread across 96 cells means the pack delivers 2% less than the sum of its cells until balanced. Passive balancing at a few hundred milliamps takes hours — which is acceptable, because a parked vehicle has hours.

The topology. A single half-bridge leg with an inductor on the battery side serves both directions:

The same two devices, the same inductor, the same duty ratio relationship — only which device is modulated changes. It is the two-quadrant chopper of Set 17 with the machine replaced by a battery, and the transition between directions is seamless because the inductor current simply crosses zero.

The duty ratio range:

A comfortable range around 0.5 — nowhere near the extremes where a boost converter's efficiency and right-half-plane zero cause trouble. Choosing the link voltage well above the pack's maximum is what buys that comfort.

The inductor, for 20% ripple at the worst case:

Only a hundred microhenries — but carrying 423 A. That combination is what makes it hard: the core must not saturate at 465 A peak, and the winding must carry 423 A with the skin and proximity effects of Set 24 at 20 kHz. It is the exact mirror of the PV inductor in Set 37 — 4.6 mH at 8.9 A.

Interleaving four phases attacks both difficulties at once:

Set 18 met ripple cancellation in a two-phase buck; here it is doing four jobs at once. The last row is particularly valuable in a vehicle, where the converter spends most of its life far below rated power — shutting down three phases removes their switching and gate-drive losses entirely.

Where the ripple cancellation is perfect:

And the operating range of 0.42–0.59 straddles the null at \(D = 0.5\) — so the input ripple is near zero at nominal state of charge and modest at the extremes. That is not a coincidence; the link voltage was chosen to put the nominal duty ratio there.

The device choice:

Silicon carbide dominates this application, and Set 39's numbers show why: at 423 A the conduction loss is everything, and a SiC MOSFET's resistive conduction beats an IGBT's fixed \(V_{CE(sat)}\) handsomely at partial load — which is where a vehicle lives.

The charger's two stages:

Isolation is a safety requirement, not a convenience: an unisolated charger would connect the pack's chassis-referenced structure directly to the mains. Set 22's isolated topologies exist for exactly this.

The turns ratio:

Choosing \(n\) so that the referred voltages match at nominal is deliberate. A DAB is most efficient when \(V_1 = V_2'\) — the circulating current grows as they diverge, which is why the pack's 40% swing is a real efficiency problem for this topology.

The power transfer law. A DAB moves power by phase-shifting one bridge's square wave against the other's:

The inductor \(L\) — usually just the transformer's leakage — is the energy transfer element, exactly as it was in the LLC of Set 29. Power flows from the leading bridge to the lagging one, so reversing the sign of \(\phi\) reverses the power. That is the whole bidirectional mechanism: one variable, both directions.

Size the inductance for rated power at a 45° shift:

Forty-two microhenries, which a transformer of this rating can provide as leakage alone — so no external inductor is needed. As with the LLC, a parasitic has become a design element.

Why 45° and not more. The power law peaks at \(\phi = \pi/2\):

Designing at 90° would leave no headroom — any dip in link voltage could not be compensated. Forty-five degrees keeps a comfortable margin while staying in the region where circulating current, and therefore conduction loss, is modest.

DAB against the LLC of Set 29:

The first row decides it for a charger that must also support vehicle-to-grid. A DAB reverses power by changing the sign of one variable; an LLC's rectifier is a diode bridge and cannot. The CLLC — a symmetric resonant tank on both sides — is the LLC's bidirectional answer, and modern chargers increasingly use it.

The complete 11 kW specification:

The currents:

Eight hundred and seventy-five amps through a cable a person must lift and plug in. That number alone is why 800 V architectures exist — it is at the edge of what liquid cooling can manage in a handheld connector.

The loss ratio:

Four times the conduction loss for the same delivered power, in every resistive element: the cable, the connector, the contactors, the busbars, the device channels and the motor windings. It is the same argument that put transmission lines at hundreds of kilovolts, applied inside a car.

What that buys, item by item:

The fourth row is a quiet but decisive advantage. At 400 V the natural device is a 650 V part, where silicon IGBTs and MOSFETs remain competitive; at 800 V it is a 1200 V part, where SiC's advantage over silicon is large. The architecture change and the device change reinforce each other.

And what it costs:

The third row is the practical obstacle. Most installed public chargers are 400 V class, so an 800 V vehicle must be able to accept them — solved either with an extra boost converter or, elegantly, by reconfiguring the traction inverter and motor windings as a boost stage during charging, using hardware the car already carries.

The charging standards landscape:

The division is about mass. An onboard charger must be carried everywhere and is therefore limited to a few tens of kilograms; a DC charger sits on the ground and can weigh whatever it needs to. That is why DC charging bypasses the vehicle's converter entirely and talks straight to the pack.

What limits charging speed in practice. Not the converter:

A well-designed 350 kW charger will still deliver far less than 350 kW to a cold pack, because the battery management system limits the current to protect the cells. Vehicles now pre-condition the pack en route to a charger for exactly this reason — heating the battery so it can accept the power on arrival.

The connected load:

Comparable with a small factory, appearing at a motorway service area or a supermarket car park — locations whose existing supply was sized for lighting and refrigeration. The connection upgrade, not the chargers, is usually the dominant project cost.

What makes it harder than a factory load:

The fourth row is the economic problem. Paying for a 1.4 MW connection that is used at 15% capacity factor is expensive, which is precisely the gap that on-site storage fills.

Buffering with stationary storage. Size a battery to cover a charging session from a modest grid connection:

A 370 kWh buffer — about five vehicle packs — lets a 300 kW connection serve a 1.4 MW site, recharging between sessions. The economics compare the storage cost against the connection upgrade, and at many sites the battery wins outright.

Vehicle-to-grid inverts the relationship. A parked fleet is a large distributed battery:

Read the first and third rows together. Frequency response pays best and cycles the battery least — a few kilowatt-hours moved back and forth per day — while arbitrage pays least and consumes real cycle life. The economics therefore favour the service that barely touches the battery.

The cost to the battery, which V2G proposals often understate:

Nearly seven pence per kilowatt-hour of throughput, before any efficiency loss — which exceeds the arbitrage spread in most markets. That single figure explains why V2G deployment has concentrated on frequency response and why energy arbitrage from vehicle batteries remains largely theoretical.

What makes it work anyway:

The third row deserves emphasis. Simply choosing when to charge — overnight rather than at the evening peak — delivers most of the grid benefit of V2G with none of the extra cycling. Unidirectional smart charging is the low-hanging fruit, and V2G is the refinement.

State of charge estimation. No sensor measures it directly, so it must be inferred:

Coulomb counting is accurate in the short term and drifts without bound — the same integrator problem as the sensorless flux estimator of Set 35. Combining it with an OCV correction in a Kalman filter gives the short-term accuracy of the integral with the long-term anchoring of the measurement.

The pre-charge problem. Closing a contactor onto a discharged link capacitor is a short circuit:

The contactor welds shut, which is a dangerous failure: a welded main contactor cannot disconnect the pack in a crash or a fault. Pre-charge is a safety system, not merely a component protection.

The pre-charge circuit:

Exactly half the energy delivered ends up in the resistor regardless of its value — a classic result. Forty joules in 150 ms is 267 W average, so the resistor is rated for a pulse rather than continuously, exactly like the soft starter of Set 30 and the wind chopper of Set 38.

The contactor sequence:

Step 3's check is essential. If the link voltage does not rise, something is drawing current — a short in the inverter, a failed capacitor — and closing the main contactor onto that fault would be destructive. The pre-charge doubles as a diagnostic.

Isolation monitoring. The pack floats relative to the vehicle chassis:

Measured continuously, because a single insulation failure is not itself hazardous — a floating system tolerates one fault — but a second one completes a circuit through the chassis. The monitor's job is to catch the first fault before the second arrives, which is the same philosophy as an IT earthing system in a hospital.

The complete BMS:

The last functional row is what actually governs the vehicle's behaviour: the BMS publishes a maximum permitted current that varies with temperature and state of charge, and every converter in the vehicle obeys it. The 350 kW charger of Problem 4 delivers whatever the BMS allows.