This study discusses the implementation of a fully decentralised optimisation for the multi-area dynamic economic dispatch of large-scale power systems based on the cutting plane consensus (CPC) algorithm. Each area constructs a local master problem to approximate the original problem by generating its own cutting planes and receiving cutting planes from other areas, hence an upper-level coordinator is not required. Two modifications of the standard CPC algorithm have been developed. First, only the newest cutting planes are transmitted among different areas to reduce the amount of information transferred. Second, to reduce the required number of iterations, a cutting plane is deleted only if it is inactive over consecutive iterations. Theoretically, the convergence and correctness of this algorithm can be guaranteed for power systems with a wide range of scales without tuning the optimisation parameters, and a high-quality suboptimal solution can still be obtained if the algorithm is prematurely terminated. The proposed method is applied to simulations of a three-area IEEE Reliability Test System and an actual four-area 2298-bus provincial power system to demonstrate its effectiveness.