Power units and hybrid systems

Power Unit Architecture and Performance Modelling in Formula One

The modern Formula One power unit (PU) is a tightly integrated thermodynamic system consisting of a high-efficiency internal combustion engine (ICE) coupled with dual electric motor-generators and sophisticated control electronics. Since 2014, technical directives have enforced the hybridisation of propulsion systems, culminating in highly constrained yet optimised energy flow architectures.

System Overview

The hybrid PU comprises six core components:

1. 1.6L V6 Turbocharged Internal Combustion Engine (ICE)
2. Motor Generator Unit – Heat (MGU-H)
3. Motor Generator Unit – Kinetic (MGU-K)
4. Turbocharger (TC)
5. Lithium-Ion Energy Store (ES)
6. Control Electronics (CE)

Each of these interacts through an optimised **energy transfer map**, constrained by fuel flow limits, maximum energy deployment, and component degradation models.

Energy Conversion Flow Model

The PU’s energy efficiency can be modelled as a closed-loop system where input chemical energy is divided into mechanical, electrical, and waste heat outputs. Total efficiency \( \eta_{\text{PU}} \) is defined as:

$\eta _{\text{PU}}={\frac {P_{\text{drive}}+P_{\text{ERS}}}{P_{\text{fuel}}}}$

Where:

• $P_{\text{drive}}$ = shaft output from ICE
• $P_{\text{ERS}}$ = net deployable power from ERS
• $P_{\text{fuel}}$ = \dot{m}_{\text{fuel}} \cdot LHV \)

- ${\dot {m}}_{\text{fuel}}$: fuel mass flow rate (kg/s), limited to 100 kg/h - LHV: Lower Heating Value of fuel (~42.6 MJ/kg)

ICE Output Modelling

Assuming ideal thermodynamic efficiency (Otto cycle), the ICE thermal efficiency is bounded by:

$\eta _{\text{th,ideal}}=1-\left({\frac {1}{r^{\gamma -1}}}\right)$

Where:

• $r$: compression ratio (~18:1 in F1 engines)
• $\gamma$: specific heat ratio (~1.33 for gasoline-air mix)

Actual ICE output torque \( T \) is derived from:

$T={\frac {P_{\text{mean}}\cdot V_{d}}{4\pi }}$

With:

• $P_{\text{mean}}$: brake mean effective pressure (BMEP)
• $V_{d}$: displacement volume (0.0016 m³)

Typical F1 ICE BMEP: ~20–24 bar under qualifying maps.

MGU-H Dynamic Transfer Model

The MGU-H converts thermal energy from turbocharger exhaust into electrical energy. In simplified terms:

$P_{\text{MGUH}}=\eta _{\text{MGUH}}\cdot {\dot {m}}_{\text{exhaust}}\cdot c_{p}\cdot (T_{turb\_in}-T_{turb\_out})$

- $c_{p}$: specific heat capacity of exhaust gas (~1.1 kJ/kg·K) - \( \eta_{\text{MGUH}} \): 30–38% in F1 conditions - MGU-H also regulates turbo RPM: up to 125,000 rpm

This electrical power is transferred either directly to the MGU-K or to the Energy Store (ES).

MGU-K Deployment Curve

The MGU-K harvests up to 120 kW during braking and redeploys up to 4 MJ per lap. Optimal deployment maximises traction-limited exit speed, particularly in low-speed corners.

MGU-K deployment strategy is defined by:

$E_{\text{K,deploy}}=\int _{0}^{t_{\text{lap}}}P_{\text{K}}(t)\cdot \delta (t)\,dt$

- $\delta (t)\in \{0,1\}$: deployment status function - Controlled by SOC maps (State-of-Charge), ERS blending strategies, and gearshift timing

Thermomechanical Constraints

The efficiency of ERS is bottlenecked by:

• Inverter thermal load: >100°C under regen
• Lithium-ion battery discharge envelope (C-rate)
• Charge air cooling effectiveness (for ICE knock control)

Heat rejection limits PU performance at high ambient tracks like Mexico City and Singapore. Engineers optimise:

• Radiator inlet pressure drop
• Intercooler latent capacity
• Surface area vs frontal drag trade-off

Powertrain Efficiency Table

Subsystem	Conversion	Peak Efficiency (%)
ICE (Shell fuel)	Chemical → Mechanical	49.8
MGU-H	Heat → Electric	35–38
MGU-K	Kinetic ↔ Electric	90–94
ES (Li-ion)	Electrical Storage	~95
Combined Lap Efficiency	Total energy recovery + delivery	46–50

Control Electronics and Mode Switching

PU logic is encoded in the Control Electronics (CE) unit, which handles:

• Strat mode selection (maps torque, fuel mix)
• SOC (State-of-Charge) ERS curves
• Torque fill blending (MGU-K + ICE)
• Traction-limited energy blending
• Deployment overtake modes (e.g., Strat 10, Strat 5, ‘Attack’)

Teams run **lap-specific energy trace simulations** to maximise usable ERS within FIA constraints.

Future Regulation (2026) Impact Model

Changes in 2026 include:

• Removal of MGU-H
• MGU-K power tripled to ~350 kW
• >50% of lap energy to be electric
• Synthetic fuels mandated

These changes imply:

$P_{\text{elec,lap}}>P_{\text{ICE,lap}}$

requiring reallocation of cooling mass flow, battery placement, and control logic redesign for KERS-only systems.

See Also

• ERS Deployment Strategy
• Turbocharger Aeroelasticity
• FIA Fuel Flow Metering Model
• Hybrid Thermal Management
• FIA 2026 PU Regulations – Technical Summary

References

• FIA Technical Regulations 2024 & 2026 Draft
• Mercedes-AMG HPP White Paper on PU Thermal Efficiency (2023)
• AVL RACING: “PU Simulation Techniques under Budget Constraints”, 2022
• Honda Racing Tech Briefing: MGU-H Torque and Vibration Suppression
• Racecar Engineering (Vol. 33 No. 4): “Heat Rejection vs Aero Compromise”
• AMuS Archives: “ERS Deployment by Circuit – Comparative Trends (2023)”