Techno-Economic and Carbon Payback Assessment of an ICE-to-EV Institutional Shuttle Fleet with Distributed PV–BESS Charging Sized via Closed-Form KKT Active-Constraint Analysis

Institutional shuttle fleets with fixed routes and predictable terminal parking are well suited to dedicated photovoltaic–battery (PV–BESS) charging infrastructure, yet siting and sizing are usually solved numerically without clear interpretation of the governing constraints. This study develops a closed-form active-constraint sizing rule, derived via Karush–Kuhn–Tucker (KKT) analysis under verified monotonicity of the net-present-value (NPV) objective over the feasible design region, for a 10-van electric academic shuttle fleet operating between the Huay Kaew and Doi Saket campuses of Rajamangala University of Technology Lanna, Chiang Mai, Thailand. One centralized station is compared with two distributed stations under reliability, cost, solar-fraction, autonomy, charger, budget, and rooftop-area constraints. The two-station configuration eliminates 47,600 km/year of dead-run travel and increases system NPV from USD 36,980 to USD 86,293 after the year-10 BESS replacement cost. The KKT analysis identifies two binding constraints—BESS one-day autonomy and PV rooftop area—giving 30 kWp PV and 94.85 kWh BESS per station, rounded to 100 kWh. The full transition achieves IRR = 12.9%, simple payback = 6.1 years, and 95.9% annual CO₂ reduction. Monte Carlo simulation with 5,000 scenarios yields P(NPV > 0) = 100% within the simulated scenario set, VaR_5% = USD 28,959, and CVaR_5% = USD 21,248, confirming financial robustness under the adopted uncertainty ranges.