Smart-port decarbonisation requires operations-research decision support under day-ahead uncertainty. We present a rolling-horizon Model Predictive Control Energy Management System, formulated as a Mixed-Integer Linear Program with five forecast streams, and benchmark it against a deterministic rule-based controller on an identical configuration. A full-year proof-of-concept at the Port of Ancona (8760 hourly steps over the 2024 Italian Day-Ahead Market, 6.5 MWp PV, 1.0 MWh BESS) combines realised 2024 market, photovoltaic and auxiliary-demand series with a post-AFIR projected cold-ironing demand—the dominant load—and is therefore an operational proof-of-concept rather than a fully metered baseline. The principal MPC outcome is structural: anticipatory dispatch raises the mean BESS state of charge from 13.6% to 46.0% and cuts residence at the minimum SoC from 81% to 6% of hours. The forecasting layer attains sub-7% sMAPE on cold-ironing-loaded demand and 9–18% on the remaining streams (seasonal MASE₂₄ ≤ 0.74 on demand and price streams). At the relay-constrained 0.08 C pilot, the realised savings is 0.44% (€14,463 yr⁻¹; 95% moving-block bootstrap CI [€12,842, €15,742]); benchmarked against an enhanced rule-based controller that is itself permitted price-threshold grid charging, the residual value of predictive optimisation is €5652 yr⁻¹ (0.17%), with the remainder of the gap being the value of enabling grid charging. A C-rate sweep shows the savings doubling to 0.93% at 0.5 C, and a direct 20 MWh/±10 MW simulation yields a €0.57 M yr⁻¹ gross arbitrage savings whose net value, after a realistic battery-degradation penalty, is substantially smaller. Controller-level operational CO₂ rises marginally (+6.2 t, +0.13%), an effect distinct from—and dwarfed by—the system-level cold-ironing decarbonisation. The framework is reproducible in open-source Python (PuLP/HiGHS) from the actual data and is portable to other single-node smart city energy hubs.