Port operators must now reduce emissions without weakening the reliability of cargo-handling and logistics services. Two load groups are especially important in this setting: vessels connected to shore-side facilities during berthing and heavy-duty vehicles working inside the terminal area. Their energy-use patterns shape both dispatch stability and the carbon intensity of the port energy system. This paper therefore proposes an integrated port energy management model that jointly schedules wind power, photovoltaic generation, hydrogen production and storage, shore power, conventional purchases, berthed-vessel demand, and low-carbon heavy-duty transport demand. The model combines price-based demand response with a tiered carbon-trading penalty so that flexible electricity consumption and emission costs are reflected in the dispatch decision. Numerical simulations show that the joint use of demand response and the carbon-penalty mechanism lowers total economic dispatch cost by about $11.05\%$ and reduces carbon emissions by $24.52\%$. The results indicate that coordinated renewable-energy and logistics-aware scheduling can improve the economic and environmental performance of port operations.