Load variability
A mean current cannot reproduce mean I² loss. Interval currents or a representative load-duration distribution are better for variable duty.
Engineering
Cable Sensitivity Calculator
Compare baseline and scenario cable loss while separating current-squared effects from route-length and temperature-adjusted resistance effects.
LOSS DRIVER SENSITIVITY
Separate current-squared exposure from route and temperature changes
This calculator is for engineers comparing how a feeder loss estimate responds to changes in load current, route length, and conductor temperature. It preserves one baseline, adjusts resistance with an entered temperature coefficient, and reports the combined I²R consequence alongside isolated current and path-resistance effects. It is a scenario model, not a substitute for a cable thermal solver or time-series load study.
Combined loss change—
Baseline loss (kW)—
Scenario loss (kW)—
Scenario current (A)—
Path resistance change—
Isolated current² effect—
LOSS DRIVER SENSITIVITY
Cable loss sensitivity decomposition
Use the driver separation to identify which evidence deserves refinement. If current dominates, collect interval current and harmonics; if path resistance dominates, verify route, conductor temperature, joints, and AC resistance.
| Sensitivity layer | Baseline | Entered change | Scenario state | Loss consequence |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
Ploss = nI²R; Is = Ib(1 + ΔI); Rs = Rb(1 + ΔL)[1 + αΔT]; ΔPloss = (Is²Rs / Ib²Rb − 1) × 100%
The method keeps the I² dependence explicit. Current, route length, and temperature-adjusted material resistance are changed independently and then recombined, so a current increase is not mistakenly treated as a linear loss increase.
Intermediate values remain unrounded until display formatting.
HOW TO USE THIS MODEL
Test one credible cable-loss scenario at a time
- Record a baseline current, one-way length, resistance basis, conductor material, and phase arrangement.
- Enter current change from a defined operating scenario rather than an arbitrary round percentage.
- Use length change only for a genuine route alternative and temperature change only for a stated thermal case.
- Confirm the temperature coefficient matches the conductor material and the resistance reference basis.
- Compare isolated current-squared and path-resistance effects before acting on the combined loss change.
LOSS DRIVER SENSITIVITY FUNDAMENTALS
Sensitivity concepts for conductor loss
- Baseline
- Documented reference state from which all changes are measured.
- Current exponent
- Conductor heat follows current squared, so a 10% current increase causes about 21% more I² loss before resistance changes.
- Length effect
- Resistance rises approximately in proportion to conductor length for unchanged material and area.
- Temperature coefficient
- Fractional resistance change per degree relative to the declared reference condition.
- Interaction
- Current and resistance effects multiply; their combined percentage is not a simple sum.
- Scenario credibility
- Physical plausibility and evidence for the entered changes, separate from arithmetic correctness.
MODEL AND FORMULA
Decompose the multiplicative I²R change
Ploss = nI²R; Is = Ib(1 + ΔI); Rs = Rb(1 + ΔL)[1 + αΔT]; ΔPloss = (Is²Rs / Ib²Rb − 1) × 100%
The method keeps the I² dependence explicit. Current, route length, and temperature-adjusted material resistance are changed independently and then recombined, so a current increase is not mistakenly treated as a linear loss increase.
SYMBOLS AND DEFAULT CASE
Variable definitions, units, and starting assumptions
| Symbol or input | Meaning | Unit or default |
|---|---|---|
| P_loss | Conductor loss for the stated phase path | kW |
| I_b | Baseline line current | A |
| I_s | Scenario line current | A |
| R_b | Baseline conductor path resistance | ohm |
| R_s | Scenario path resistance | ohm |
| alpha | Resistance temperature coefficient | per degree C |
| baseCurrentA | Baseline current (A) | 220 |
| baseLengthM | Baseline one-way length (m) | 160 |
| baseResistanceOhmPerKm | Baseline resistance (ohm/km) | 0.153 |
| currentChangePercent | Scenario current change (%) | 15 |
| lengthChangePercent | Scenario length change (%) | 8 |
| temperatureChangeC | Conductor temperature change (°C) | 20 |
| temperatureCoefficientPercentPerC | Resistance coefficient (%/°C) | 0.393 |
| phases | Circuit phases (1 or 3) | 3 |
Percent inputs are converted to decimal factors once. The live calculation process above substitutes the current values in order, names intermediate quantities, reports the final result, and closes with a reverse or conservation check.
DEEP ENGINEERING ANALYSIS
Interpret the drivers before selecting a mitigation
Resistance basis
DC resistance, operating-temperature resistance, and effective AC resistance answer different questions; mixing them obscures the real driver.
Thermal coupling
Temperature affects resistance while loss affects temperature. This one-pass model does not iterate to a thermal equilibrium.
WORKED DECISION CASES
Two sensitivity questions
Production expansion
A 15% current increase causes more than a 15% loss increase before the warmer conductor is considered, focusing attention on interval load and ventilation.
Alternative cable route
A longer route increases path resistance, but a larger conductor reduces base resistance. The alternatives are compared as separate documented scenarios rather than one blended guess.
TECHNICAL GLOSSARY
Cable sensitivity terms
- Sensitivity
- Change in output associated with a stated input change.
- Baseline resistance
- Resistance value tied to the reference conductor condition.
- Scenario ratio
- Scenario value divided by baseline value.
- Temperature coefficient
- Material-specific fractional resistance change per degree.
- Interaction term
- Extra combined effect created when multiple multipliers change together.
- Elasticity
- Approximate percentage response of an output to a one-percent input change near a point.
EVIDENCE AND DATA LINEAGE
Retain the reference state and each scenario cause
Record baseline current timestamp or load case, phase basis, conductor material and size, resistance type and reference temperature, physical route length, operating temperature evidence, coefficients and units, scenario rationale, interval load data when available, and unrounded loss ratios.
LIMITS AND EXCLUSIONS
What this sensitivity model excludes
- It does not solve conductor temperature, ampacity, voltage quality, harmonics, skin effect, proximity effect, joint resistance, or neutral loading.
- It treats resistance as linear with temperature over the entered range and assumes material and cross-section do not change.
- It evaluates one combined scenario and does not assign probabilities or tolerances.
RELIABLE SOURCES
References for this method and its boundaries
FREQUENTLY ASKED QUESTIONS
Cable sensitivity questions
Why is the current effect squared?
Joule heating is I²R, so current acts twice in the loss ratio.
Can the current change be negative?
Yes, provided scenario current remains positive.
Why not add the three percentage effects?
Length and temperature alter resistance and then multiply the current-squared ratio; simple addition omits interaction.
Does temperature change mean ambient temperature?
It means conductor temperature change. Ambient may influence conductor temperature but is not identical to it.
Can this predict final conductor temperature?
No. That requires a thermal model with heat transfer and installation conditions.
Should I use one result for annual energy?
Only for a stable duty. Variable current requires time-weighted I² integration.
IMPORTANT ENGINEERING NOTE
Sensitivity ranks questions; it does not certify the cable
Use the result to prioritize measurements and alternatives. Final engineering requires verified AC resistance, load profile, cable thermal conditions, protection and fault checks, voltage-drop assessment, manufacturer data, and the governing electrical code.