Lightweight Calculation Method for Heating Loads in Existing Residential Clusters via Spatial Thermal Pattern Decoupling and Matrix Reorganization

Centralized heating systems in severe cold regions suffer from widespread load estimation deviations due to architectural heterogeneity and a lack of construction drawings, leading to substantial energy waste. This study proposes a lightweight load calculation method that facilitates efficient calculation of heating loads for heterogeneous building clusters via spatial thermal pattern decoupling and matrix reorganization. First, a 3 × 3 load characteristic matrix is developed to characterize the spatial variation in thermal demand across different building positions (corner vs. intermediate units × top, middle, and bottom floors), revealing that corner units exhibit higher thermal loads than intermediate units, while top and bottom floors show significantly higher loads than middle floors. Second, two complementary matrices are established: the load characteristic matrix, which represents the building’s thermal behavior, and the structural feature matrix, which encodes the architectural configuration in terms of unit count (a) and floor count (b). Together, they enable rapid hourly load synthesis using only lightweight input parameters. The method is validated on 56 heterogeneous residential buildings in Northeast China. Using a decoupled 4U/6F standard model, the synthesized cluster heating load achieves an R2 of 0.88, an RMSE of 24.15 GJ, a MAPE of 4.94%, and a Mean Percentage Error (MPE) of −0.82% against actual heating supply data, demonstrating high accuracy and negligible systematic bias—particularly during cold waves. This approach allows the seasonal variation in heat demand across an entire residential area to be estimated even in the absence of detailed construction drawings, offering practical guidance for operational heating management.