Probabilistic carbon emission flow calculation of power system with Latin Hypercube Sampling

To quantify the impact of renewable energy uncertainty on carbon emission flow (CEF), this paper proposes a probabilistic CEF calculation method based on Latin Hypercube Sampling (LHS). Traditional Monte Carlo Simulation (MCS) methods typically combine with Simple Random Sampling (SRS), but such methods are less efficient in handling high-dimensional problems, with limited coverage of the input random variable distribution space. To address this issue, this paper introduces an MCS method combined with LHS and Gram-Schmidt sequence orthogonalization (GS-LHS). The GS-LHS method systematically distributes sample points, making the sample distribution more uniform in multi-dimensional space, while the Gram-Schmidt sequence orthogonalization further improves sampling efficiency and coverage. Based on the proposed method, this paper conducts a detailed analysis of the IEEE 14-bus and 118-bus systems, using MATLAB for simulation and calculating the probabilistic distribution of node carbon intensity (NCI) for each node. The analysis results show that the proposed method can provide more accurate NCI probability distribution estimates with fewer samples. In the IEEE118 system, with 10³ samples, the proposed method's average relative error is 0.1489 % (max 1.1458 %), while SRS has an average of 0.2155 % (max 5.9098 %). The GS-LHS method requires only 46.52 % of the sample size and 47.17 % of the computation time of the SRS method at a 1 % error threshold, resulting in a total time saving of approximately 45.36 %. This shows that the proposed method surpasses SRS in estimating the distribution of output random variables, also maintains the simplicity and flexibility of MCS and reduce the computation time.