🎓 Lesson 17
D5
Electric Drive Efficiency Mapping for Payload-Dependent Duty Cycles
Electric drive efficiency mapping shows how efficiently an autonomous haul truck’s electric motor converts battery power into wheel motion—depending on how heavy its load is and what terrain it’s climbing.
🎯 Learning Objectives
- ✓ Calculate drive system efficiency at a given payload, speed, and grade using interpolated efficiency maps
- ✓ Analyze how payload-dependent torque–speed operating points shift across efficiency isocontours
- ✓ Design a simplified 3D efficiency lookup table (payload × speed × grade) for a 220-ton autonomous haul truck
- ✓ Explain the thermal implications of sustained operation in low-efficiency 'corner' regions of the map
📖 Why This Matters
In autonomous haulage systems (AHS), energy efficiency directly determines battery size, charging infrastructure cost, fleet uptime, and total cost of ownership. A 2% drop in average drive efficiency across a 50-truck fleet can increase annual grid demand by >8 GWh—and trigger thermal derating that reduces payload capacity on hot, steep ramps. Efficiency isn’t fixed: it changes with payload, because torque demand scales linearly with mass, shifting the motor’s operating point across its non-uniform efficiency landscape. Mapping this relationship isn’t academic—it’s the foundation for predictive energy dispatch and thermal-aware path planning.
📘 Core Principles
Electric drive efficiency (η) is defined as mechanical output power divided by DC input power: η = P_mech / P_dc. Unlike internal combustion engines, electric drives exhibit peak efficiency (>95%) near rated torque and medium speed—but efficiency drops sharply at low torque (light payloads, flat hauls) due to fixed inverter switching losses and motor iron losses dominating, and at high torque–low speed (heavy payloads, steep grades) due to increased copper losses and thermal saturation. Payload alters the required tractive effort (F_traction = m·g·(sinθ + C_r) + ½ρ·C_d·A·v²), which—via axle ratio and wheel radius—sets motor torque and speed. Thus, payload defines a family of operating trajectories across the motor’s torque–speed plane; each trajectory intersects different iso-efficiency contours. Thermal effects further modulate efficiency: continuous operation above 85°C stator winding temperature degrades insulation life and forces active derating, lowering effective η.
📐 Efficiency Interpolation from 3D Map
For real-time energy modeling, efficiency is interpolated from a discrete 3D map η(Payload, v, grade). Linear trilinear interpolation balances accuracy and computational load in onboard controllers.
💡 Worked Example
Problem: Given a 220-ton haul truck at 35 km/h on a 6% grade with 185 t payload. Efficiency map nodes: η(170 t, 30 km/h, 4%) = 91.2%; η(170 t, 30 km/h, 8%) = 89.5%; η(170 t, 40 km/h, 4%) = 92.1%; η(170 t, 40 km/h, 8%) = 90.3%; η(200 t, 30 km/h, 4%) = 90.8%; η(200 t, 30 km/h, 8%) = 88.9%; η(200 t, 40 km/h, 4%) = 91.7%; η(200 t, 40 km/h, 8%) = 89.9%. Interpolate η at (185 t, 35 km/h, 6%).
1.
Step 1: Normalize coordinates: payload fraction = (185−170)/(200−170) = 0.5; speed fraction = (35−30)/(40−30) = 0.5; grade fraction = (6−4)/(8−4) = 0.5
2.
Step 2: Apply trilinear interpolation across 8 corner nodes — compute weighted sum using volume fractions. For brevity, result uses standard trilinear formula: η = Σ w_i · η_i where w_i are eight volumetric weights.
3.
Step 3: Computed η = 0.125×(91.2 + 89.5 + 92.1 + 90.3 + 90.8 + 88.9 + 91.7 + 89.9) = 90.55%
Answer:
The interpolated efficiency is 90.55%, which falls within the typical operational range of 88–93% for this class of drive under mixed-duty conditions.
🏗️ Real-World Application
At Rio Tinto’s Gudai-Darri mine (Western Australia), Komatsu 930E-SE autonomous trucks use payload-dependent efficiency maps embedded in their Fleet Intelligence™ energy optimizer. During commissioning, dynamometer tests revealed that at 50% payload (110 t), efficiency dropped to 87.3% on 10% grades due to excessive slip loss and inverter overmodulation—prompting firmware updates to limit torque slew rate and activate regenerative braking earlier. This adjustment improved average cycle efficiency by 1.8% and reduced inverter coolant temperature excursions by 12°C—extending IGBT lifetime by ~14,000 hours per unit.
🔧 Interactive Calculator
🔧 Open Autonomous Haulage Systems Integration Calculator📋 Case Connection
📋 Coal Mine Battery Thermal Management at BHP Mt Arthur
Battery pack thermal runaway risk during 12hr shifts; SOC estimation drift >8% after 4 hours