For novel power systems, access to sustainable energy sources will undoubtedly increase the uncertainty of power systems significantly. Consequently, to guarantee efficient, secure, smooth, and expedited functioning, this work proposes a matrix Wasserstein distance generative adversarial network with gradient penalty (MWGAN-GP), which considers the minimization of generation cost and carbon emission simultaneously for low-carbon economic dispatch (ED) of novel power systems. The proposed MWGAN-GP generates a series of matrix data by a trained generator, equalizes load values and the sum of unit outputs at each period by relaxation operation, and rapidly generates numerous ED solutions. The speed of ED based on MWGAN-GP is greatly faster than the speed of ED based on a traditional genetic algorithm (GA). Furthermore, the introduction of the relaxation operation decreases the average cost of ED based on MWGAN-GP by 7.94 % compared to GA according to the case with 4000 sets of load data.