Renewable Energy Payback: Carbon Debt vs Avoided Emissions (2D)

Installation

System size 5 kW

Displaced grid carbon intensity 450 g/kWh

Years per second 2

Simulated year

0.0

Embodied carbon debt

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Cumulative avoided CO2

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Net balance

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Carbon payback

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Net savings @ 25 yr life

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How it works

Manufacturing, transporting and installing a solar array or wind turbine burns real energy — usually from a fossil-heavy grid — before it displaces a single gram of grid emissions. The engine tracks two real numbers as simulated years pass:

debt_kg      = embodied_kWh_per_kW × size_kW × mfg_grid_intensity
avoided_kg   = Σ (annual_output_kWh × grid_intensity) over elapsed years   (numerically integrated)
payback_year = t where avoided_kg(t) crosses debt_kg   (found by root-finding on the integrated curve)

The chart plots the actual cumulative-avoided-emissions trajectory sampled frame by frame, not a closed-form shortcut — the crossing marker is placed by linearly interpolating between the two samples that straddle the debt line, the same way a numerical solver brackets a root.

Displaced grid carbon — a coal-heavy grid (~800-900 g/kWh) pays back the embodied carbon far faster than an already-clean one (~50-150 g/kWh), because each avoided kWh is worth more. Drag it up and watch the payback marker slide left.
System size — scales embodied debt and annual output together, so it does not change the payback time, only the absolute tons of CO2 on both axes.
Default assumptions — Solar PV: 1900 kWh/kW embodied, capacity factor 18%. Wind: 1500 kWh/kW embodied, capacity factor 34%. Manufacturing itself assumed to run on a ~500 g CO2/kWh grid.
Net lifetime savings — avoided emissions accumulated over a 25-year operating life minus the upfront debt, read directly off the simulated trajectory (extrapolated at the current avoided-rate for years not yet simulated).

Year 0.0

Cumulative avoided CO2 Embodied carbon debt