🎓 Lesson 16
D5
Total Cost of Ownership Model: Energy Losses, Maintenance, and Scrap Value
Total Cost of Ownership (TCO) is the full lifetime cost of an electrical cable — including what you pay to buy it, how much energy it wastes over time, how often you must repair or replace it, and how much money you get back when you scrap it.
🎯 Learning Objectives
- ✓ Calculate the 20-year net present value (NPV) of energy losses for a given cable size and load profile
- ✓ Design cable cross-sectional area to minimize TCO while meeting IEEE 835 and IEC 60287 ampacity constraints
- ✓ Analyze maintenance cost escalation trends using historical mine fleet data and failure rate models
- ✓ Explain how scrap value recovery offsets depreciation and influences end-of-life replacement decisions
- ✓ Apply TCO sensitivity analysis to evaluate trade-offs between copper vs. aluminum conductors in mobile substation feeders
📖 Why This Matters
In open-pit mines, a single 3.3 kV trailing cable feeding a hydraulic shovel can consume over 1.2 GWh/year in resistive losses — costing $150,000+ annually in electricity alone. Yet procurement teams often select cables based solely on minimum code-compliant ampacity, ignoring decades of hidden losses. This lesson reveals how TCO modeling transforms cable selection from a compliance exercise into a strategic capital decision — directly impacting mine operating costs, carbon footprint, and equipment uptime.
📘 Core Principles
TCO rests on four interdependent pillars: (1) Energy losses scale quadratically with current and inversely with conductor cross-section (I²R); (2) Maintenance costs follow a bathtub curve — low early, peaking at insulation aging thresholds (~12–15 years for EPR/HEPR in abrasive haul roads); (3) Scrap value depends on conductor material purity, weight, and real-time commodity prices (e.g., LME copper futures); (4) Discounted cash flow (DCF) is required to compare costs across a 20–30 year lifespan, as $1 spent today ≠ $1 spent in year 15. Ampacity optimization occurs where marginal cost of larger cable equals marginal savings in energy + maintenance — not where temperature rise hits 90°C.
📐 TCO Lifecycle Cost Model
The TCO model sums discounted cash flows across all cost categories over n years. Energy loss cost dominates for high-load, continuous-duty circuits like dragline feeds or in-pit substations. The key formula isolates annual energy loss cost — the most sensitive lever in ampacity optimization.
Annual Energy Loss Cost
C_energy = 3 × I² × R × 8760 × C_kWhMonetizes resistive (I²R) losses in a 3-phase AC system over one year.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| I | Line current | A | RMS current per phase under typical load |
| R | Conductor resistance per phase | Ω | DC resistance adjusted for skin/proximity effect (IEC 60287) |
| C_kWh | Electricity cost | $/kWh | Mine-specific blended rate including demand charges and grid losses |
Typical Ranges:
Continuous-duty dragline feeder: 200 – 600 A
Haul truck trailing cable: 150 – 450 A
💡 Worked Example
Problem: A 1.2 km, 3.3 kV, 3-core 240 mm² Cu XLPE cable supplies a shovel drawing 320 A RMS continuously. System PF = 0.85, electricity cost = $0.11/kWh, discount rate = 5%, 20-year life. Resistivity ρ = 1.724×10⁻⁸ Ω·m, k = 1.0 (for 3-phase balanced). Calculate annual energy loss cost.
1.
Step 1: Compute resistance per phase: R = ρ × L / A = (1.724e-8) × 1200 / (240e-6) = 0.0862 Ω
2.
Step 2: Compute 3-phase power loss: P_loss = 3 × I² × R = 3 × (320)² × 0.0862 = 26,603 W ≈ 26.6 kW
3.
Step 3: Annual energy loss = 26.6 kW × 8760 h/yr = 233,016 kWh/yr → Cost = 233,016 × $0.11 = $25,632/yr
Answer:
The annual energy loss cost is $25,632 — which exceeds the cable’s initial purchase cost ($18,500) within 1.8 years. Over 20 years (5% discount), NPV of losses = $327,400 — justifying upgrade to 400 mm² if it reduces losses by ≥35%.
🏗️ Real-World Application
At Rio Tinto’s Pilbara iron ore operation, TCO analysis of 6.6 kV dragline feeder cables revealed that upgrading from 300 mm² to 500 mm² Cu reduced lifetime energy losses by 41%, extended mean time between failures (MTBF) from 8.2 to 14.7 years, and yielded a 3.2-year ROI despite 68% higher CAPEX. Scrap recovery of 92% pure copper at end-of-life contributed $22,000 toward replacement cost — validated via on-site metal assay and LME settlement pricing.
📋 Case Connection
📋 Data Center Electrical Design: 40 MW Hyperscale Facility in Singapore
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