Data-Physical Hybrid Driven Distribution Network Linear Power Flow Considering Non-Smooth Constraints

Existing liner power flow (LPF) models do not consider the non-smooth constraint characteristics of the voltage source converter (VSC) and on-load tap changer (OLTC) that contain operation limit and dead zones, which limits its application. Thus, a three-phase LPF model for distribution networks is proposed, which considers non-smooth constraint characteristics. Firstly, smoothing functions are used to effectively fit the non-smooth constraint characteristics, resulting in control functions that are continuous and differentiable. Then, based on the first-order Taylor series expansion, the three-phase power flow equations are physically linearized, and the terms to compensate errors are obtained through the partial least squares (PLS) method. Compared with the model without considering the non-smooth constraints, the three-phase LPF model considering the non-smooth constraints can accurately represent the operating characteristics of the VSC and the OLTC in the actual distribution network, thus providing more reliable power flow calculation results. Based on a typical 42-node distribution network, the proposed model is compared and analyzed against other LPF models. The results indicate that the proposed model has the ability to handle non-smooth constraints, with higher computational accuracy compared to existing data-physical hybrid driven models.