Centralized multi-port scheduling often incurs heavy computation and slow response. This paper develops a ‘cloud-edge-end’ distributed low-carbon scheduling framework based on consistency theory for terminal equipment clusters. First

using the adjustable trapezoidal energy profile of quay cranes

a demand-response geometric programming model is built with average operating power as the decision variable

capturing quay crane power. Then

a nonlinear update for dynamic electricity price is designed by embedding renewable accommodation elasticity and an emergency impact term

enabling coordination among the port control center

edge nodes

and on-site equipment. This mechanism also internalizes carbon intensity signals and encourages renewable utilization without full information sharing. Then

a two-dimensional consistency protocol links power regulation with logistics constraints in real time. To ensure robustness under communication delays

Lyapunov-Krasovskii functionals yield delay-compensation conditions. Case studies show faster convergence and reduced system load variation

with lower emissions and electricity cost while maintaining throughput

and supporting scalable collaboration across multiple terminals.