20. Cost and Economic Calculations

Principle

Economic calculations in electrical engineering help compare options and evaluate the financial viability of projects. Typically, these analyses involve:

  • Capital Costs (CapEx): The initial cost of equipment or installation.
  • Operating Costs (OpEx): Recurring expenses such as energy and maintenance costs.
  • Life-Cycle Cost (LCC): The total cost over the system’s lifetime, typically present-valued.
  • Payback Period: The time required for savings or revenues to cover the initial investment.
  • ROI, NPV, IRR: Metrics such as Return on Investment, Net Present Value, and Internal Rate of Return are used to assess project profitability.

Life-Cycle Cost (LCC) Analysis

LCC is the sum of all costs—from purchase to disposal—discounted to present value. For example, when choosing between a low-efficiency motor and a high-efficiency motor, you would:

  • Calculate the extra purchase cost.
  • Estimate annual energy savings (kWh saved multiplied by tariff).
  • Determine the payback period (years until savings exceed the extra cost).
  • Compute the NPV: sum of discounted annual savings minus the extra cost.

In a simplified formula, total LCC is expressed as:

LCC = CapEx + Σ (OpEx × (1+i)−year)

where i is the discount rate.

Example – Lamp Replacement

A factory considers replacing 100 metal-halide lamps with LED fixtures:

  • Current System: 100 × 455W × 3000 h = 136,500 kWh/year → Cost: $13,650/year at $0.1/kWh.
  • New LED System: 100 × 200W × 3000 h = 60,000 kWh/year → Cost: $6,000/year.
    Annual energy saving: $7,650.
  • Capital Cost: LED fixtures cost $300 each plus $50 installation → Total ≈ $35,000.
  • Maintenance: Metal-halide lamps require replacement every ~3 years (average cost ~$5,000/year), whereas LED maintenance is minimal (e.g., $1,000/year for cleaning).
  • Net Annual Savings: $7,650 (energy) + ~$5,000 (maintenance) = ~$12,650/year.
  • Payback Period: $35,000 / $12,650 ≈ 2.8 years.
  • NPV: Over a 10-year life at a 5% discount rate, NPV of savings ≈ 12,650 × 7.72 ≈ $97,600; subtracting the $35,000 upfront cost yields +$62,000.

Cost of Losses

Consider a transformer with a 1 kW core loss (24/7) and a 5 kW copper loss at full load. If operated at 50% load, copper loss averages to ~1.25 kW. Total loss ≈ 2.25 kW, which over a year (≈19,710 kWh) costs about $1,971 at $0.1/kWh. A higher-efficiency unit might reduce losses by ~$1,000/year. If the extra cost is $5,000, the payback period is about 5 years, which may be favorable over a 30-year transformer life.

Reliability Cost

Downtime cost is sometimes used to justify investments in redundancy or higher reliability. For instance, if downtime costs $100k/hour and an improvement reduces expected downtime by 0.1 hour/year (saving $10k/year), one might justify a $50–100k investment depending on the discount rate.

Economic Optimization and Tariff Analysis

Additional calculations may optimize component selection. For example:

  • Optimum Cable Size: Trade the higher upfront cost of thicker cable versus lower energy losses over the cable’s life. Economic optimization finds the cable size where the derivative of LCC with respect to size is zero.
  • Tariff Analysis: Evaluate if shifting loads to off-peak times (with lower tariffs) or implementing peak-shaving (using storage or generators) can reduce costs.

ROI and IRR

ROI is calculated as (Net Benefit / Cost) and is often expressed as an annual percentage. IRR is the discount rate at which the project’s NPV is zero. If the IRR exceeds the company’s hurdle rate, the project is deemed economically viable.

Niche Costs

  • Power Factor Penalties: Calculate the cost incurred due to low PF (if the utility charges per kVAR or bases bills on kVA), and compare it to the cost of installing PF correction capacitors.
  • Carbon Costs: Incorporate a carbon price into energy costs to justify green projects.
  • Battery vs. Generator for Backup: Perform an NPV analysis comparing fuel and maintenance costs for generators versus battery replacement costs over time.

Industry Relevance

Economic calculations drive decisions for energy efficiency, reliability upgrades, and technology selections. Large organizations often require a financial justification—such as a payback period under 3 years or an IRR above 15%—before funding projects. In many cases, regulators and building codes incentivize investments that reduce energy consumption and emissions.

Standards

  • ISO 50001 (Energy Management): Encourages life-cycle cost analysis when evaluating energy performance improvements.
  • FEMP Guidelines: Provide methodologies for LCC analysis of federal projects in the US.
  • IEEE 493 (Gold Book): Includes methods for calculating the cost of power interruptions and optimizing system configurations.
  • IEC 60300-3-3: Covers life cycle costing for reliability and maintainability decisions.

Software Tools

  • Spreadsheet Models: Excel is widely used with built-in functions (NPV, IRR, etc.) to perform LCC analysis.
  • RETScreen: Free software by Natural Resources Canada for clean energy project analysis.
  • Homer Energy: Used for microgrid optimization and evaluating the economics of various energy configurations.
  • Vendor ROI Tools: Many manufacturers provide online calculators to estimate energy savings and payback for technologies like VFDs or LED lighting.
  • Building Simulation Tools: Programs like eQuest or EnergyPlus can compare energy costs between design alternatives and feed results into LCC calculations.

Conclusion

By calculating capital and operating costs, determining payback periods, and evaluating metrics like ROI, NPV, and IRR, engineers can compare design options and justify investments that lower energy costs, enhance reliability, and meet regulatory requirements. Presenting these key financial metrics allows decision-makers to understand the economic benefits of energy efficiency and reliability improvements.