Data-Driven Piecewise Linearization for Distribution Three-Phase Stochastic Power Flow

Enhancing Renewable Energy Accommodation by Coupling Integration Optimization with Flexible Retrofitted Thermal Power Plant

“…The principal decision variables are the output of the power sources: P TPU u,t for TPUs, P WT t for WT, and P PV t for PV. To address the MINLP, the big-M method [33] and the piecewise linearization method [34] are employed to reformulate the model into a mixed integer linear optimization programming (MILP) for an easier solution.…”

An improved compact-form antisaturation model-free adaptive control algorithm for a class of nonlinear systems with time delays

“…See Appendix A. Remark 1: The dynamic linearization method proposed in this article has essential differences from other linearization methods such as Feedback linearization, 26 Taylor linearization, 27 piecewise linearization, 28 etc. Firstly, the generation of PPD is not dependent on the structure and parameters of the original system, but only on the I/O data generated by the system.…”

Overview of Data-driven Power Flow Linearization

“…The former issue includes the problems caused by (i) data multicollinearity [14]- [18], (ii) the presence of outliers [16], [19]- [21], (iii) measurement noises [7], [18], [22], [23], (iv) the temporal correlation among observations [24], and (v) asynchronous data [5], [25]- [27]. The system-related issue refers to the challenges particularly related to power systems, namely (i) the inherent nonlinearity of the physical characteristics in power flows [1], (ii) the lack of consensus on the importance and usage of physical knowledge [1], [7], [28]- [30], (iii) frequent variations in grid topologies [6], [27], [31], (iv) inevitable variations in bus types [6], [32], and (iii) the limited observability of the system [15], [21], [27].…”

“…The former type adopts the classic formulations of various regression programming models, while the latter reorganizes the classic regression model by customizing the objective functions and/or constraints. Specifically, the regression DPFL approaches include (i) least squares regression and its variants [1], [3], [5], [7], [11], [14], [21], [24], [25], [27], [33]- [37], (ii) partial least squares and its variants [6], [11], [26], [38], (iii) ridge regression and its variants [15], [18], [31], and (iv) support vector regression and its variants [11], [21], [36], [39], [40]. The tailored DPFL methods consist of (i) linearly constrained programming [7], [30], (ii) chanceconstrained programming [41], and (iii) distributionally robust chance-constrained programming [42].…”