Threadmark: Mathematical Model, Units & Reproducible Benchmarks
Role & Domain Intent: Energy project economics (Discounted energy costs and ledgers; not RFQ management or tax advice.)
Equations, Variables & Dimensional Rules
Levelized energy cost from discounted cost and generation ledgers.
LCOE ($/MWh) = [ Σ_{t=0..N} (CAPEX_t + OPEX_t + Fuel_t) / (1 + r)^t ] / [ Σ_{t=1..N} E_t / (1 + r)^t ], where E_t = Capacity (MW) × 8,760 h × CF × (1 − d)^{t−1}
Declared Units: Capacity in MW; CAPEX in $/kW; OPEX in $/kW-yr; discount rate r in %; degradation d in %/yr; annual generation E_t in MWh; LCOE in $/MWh (real price-year currency).
Step-by-Step Numerical Verification
Scenario 1 (Utility Solar PV Cohort, 2027 commissioning, CAPEX = $950/kW, -2%/yr cohort capex trajectory): Discounted lifecycle cost divided by discounted energy ledger yields LCOE = $50.02/MWh for the 2027 cohort, declining to $49.18/MWh (2028), $48.36/MWh (2029), and $47.56/MWh (2030) under identical discount and capacity-factor assumptions.
| Commissioning Cohort | Plant CAPEX ($/kW) | Annual Capex Change | Discounted LCOE ($/MWh) | Scope Status |
|---|---|---|---|---|
| 2027 Cohort | 950.00 | Baseline | 50.02 | Synthetic Ledger |
| 2028 Cohort | 931.00 | -2.0% | 49.18 | Synthetic Ledger |
| 2029 Cohort | 912.38 | -2.0% | 48.36 | Synthetic Ledger |
| 2030 Cohort | 894.13 | -2.0% | 47.56 | Synthetic Ledger |
Solstice Cost Studio — Governing Equations & Worked Verification
Canonical Module URL: https://mkbiz.co.business/solar-cost/ · Launch Interactive Runtime ↗
Scope: Solar mounting/capacity cost comparisons, synthetic rate cards and discounted generation.
Boundary & Limitation: Financing, taxation and revenue are explicitly outside scope.
AC_Capacity (MW) = Capacity_MWp / (DC/AC Ratio); E_t (MWh) = Capacity_MWp × Yield (kWh/kWp) × (1 − d)^{t−1}; LCOE (GBP/MWh) = NPV(CAPEX + OPEX) / NPV(E_t)
Units & Conventions: DC capacity in MWp; AC capacity in MW; specific yield in kWh/kWp/yr; degradation d in %/yr; discount rate in %; CAPEX and OPEX in GBP; LCOE in GBP/MWh.
Worked Verification Example: Case 1 (10 MWp fixed-tilt solar plant, DC/AC ratio = 1.25 → 8.0 MW AC, specific yield = 1,300 kWh/kWp, degradation = 0.45%/yr, discount rate = 6%, inflation = 2%, 25-year life, 15 ha land): Total CAPEX = 5,335,122.72 GBP, Annual OPEX = 124,621.32 GBP/yr, and discounted LCOE = 45.79 GBP/MWh.
| Case ID | Capacity (MWp) | Mounting | Yield (kWh/kWp) | Discount (%) | CAPEX (GBP) | Annual OPEX (GBP) | LCOE (GBP/MWh) |
|---|---|---|---|---|---|---|---|
| Case 1 (Fixed Tilt) | 10.0 MWp | Fixed | 1,300 | 6.0% | 5,335,122.72 | 124,621.32 | 45.79 |
| Case 2 (Single-Axis Tracker) | 10.0 MWp | Tracker | 1,480 | 6.0% | 5,890,400.00 | 138,200.00 | 43.12 |
| Case 3 (High Discount Rate) | 10.0 MWp | Fixed | 1,300 | 9.0% | 5,335,122.72 | 124,621.32 | 54.68 |
TariffHarbor Studio — Governing Equations & Worked Verification
Canonical Module URL: https://mkbiz.co.business/charging-tariffs/ · Launch Interactive Runtime ↗
Scope: Charging-energy valuation with acquisition cost, markup, illustrative tax and margin calculations.
Boundary & Limitation: Synthetic configuration; no booking, billing, legal tax validation or real tariff feed.
C_acq = E_kWh × c_connector + c_roaming; R_net = round_half_up(C_acq × (1 + markup) + fee_session + D_min × fee_min, 0.01); Tax = round_half_up(R_net × τ_tax, 0.01); Total = R_net + Tax; Margin (%) = (R_net − C_acq) / R_net × 100
Units & Conventions: Session energy in kWh; duration in minutes; acquisition costs and fees in EUR; markup, margin, and illustrative tax in %; half-up rounding to 0.01 EUR (integer cents).
Worked Verification Example: Case 1 (DC fast-charge session: 28 kWh, 40 min, DC acquisition cost = 0.29 EUR/kWh, roaming cost = 0.40 EUR, markup = 25%, session fee = 1.00 EUR, minute fee = 0.01 EUR/min, illustrative tax = 20%, min margin policy = 8%): Net pre-tax charge = 12.05 EUR, Illustrative Tax = 2.41 EUR, Total Session Valuation = 14.46 EUR, passing the 8% minimum margin and 250 kWh / 500 EUR policy caps.
| Case ID | Connector | Energy (kWh) | Duration (min) | DC/AC Cost (EUR/kWh) | Markup (%) | Tax (EUR) | Total (EUR) | Policy Gate |
|---|---|---|---|---|---|---|---|---|
| Case 1 (Standard DC) | DC | 28.0 | 40 | 0.29 | 25% | 2.41 | 14.46 | Pass (Active) |
| Case 2 (AC Commuter) | AC | 11.0 | 120 | 0.20 | 20% | 0.97 | 5.81 | Pass (Active) |
| Case 3 (High Volume Fleet) | DC | 85.0 | 55 | 0.29 | 10% | 5.75 | 34.52 | Margin Check |
Validation Status, Scope Exclusions & Disclaimers
- Data Status: Synthetic / precomputed browser demonstration fixtures generated deterministically from the project engine.
- Operational Limitation: Not RFQ management, business accounting or investment advice.
- Client-Side Execution: All interactive views, filters, and JSON/CSV exports execute locally in the user's browser with zero external API calls, zero telemetry, and no server-side persistence.
- Author & Principal Investigator: Mohammad Rezwan Khan, PhD (Aalborg University · BESS QA/QC & Power Systems Specialist).