To account for the probability distribution information of uncertain scenarios, this letter proposes a novel interval power flow (NIPF) method based on hybrid uncertain sets. Firstly, a NIPF model is established by integrating the hybrid box-ellipsoid sets characterizing uncertainties in interval power flow (IPF), which is solved by the optimizing-scenario method (OSM). Then, a multivariate statistical analysis method (MSAM) and a chance-constrained programming-based method (CCPM) are proposed for determining the optimal radii of the ellipsoid set and side length of the box set under two scenarios, respectively, namely, the normal distributions without correlations and the arbitrary distributions with correlations. Finally, case studies validate the effectiveness and advantage of the proposed method compared with traditional IPF methods based on Monte Carlo simulation, box sets, and ellipsoid sets.

Previous robust transmission expansion planning (RTEP) studies have rarely considered the important question of how large the uncertainty set should be, and hence, how the uncertainty budget can be determined objectively. This study addresses this issue by proposing a novel adaptive optimization method that optimizes the value of the uncertainty budget to minimize the size of the uncertainty set while considering the underlying risk for wind power generation (WPG) fluctuations residing outside of the proposed uncertainty set. As such, the proposed method ensures a good tradeoff between the robustness and costs of RTEP solutions. In addition, the proposed method optimizes investment strategies under forecasted WPG scenarios, while providing a security guarantee under extreme WPG scenarios. The variable-limit integral terms introduced by the proposed method are addressed in the solution process by applying the piecewise linearization approximation method combined with the quadratic Newton-Gregory interpolating polynomial technique, which allows the solution process to be cast as a mixed integer linear programming problem. The good performance and effectiveness of the proposed adaptive uncertainty set optimization method are verified by numerical results.

This paper proposes a central limit theorem-based method (CLTM) to overcome the conservatism of interval DC and AC power flow analysis under uncertainty of renewable power generation. Interval DC power flow (IDCPF) models are solved by expressing the bus angle and active transmission power as linear combinations of interval nodal power injections, and then the central limit theorem is applied to obtain high-confidence intervals of DC power flow variables. Interval AC power flow (IACPF) models are solved by first applying the optimizing-scenarios method to acquire more accurate affine arithmetic forms of the power flow variables defined according to linear combinations of nodal power injections, and then high-confidence intervals of AC power flow variables are obtained via the central limit theorem. In addition, a criterion formulation is established to evaluate the errors of interval power flow methods. The results of simulations validate the effectiveness and superiority of the proposed method relative to the performances of previously established methods, including the Monte Carlo simulation, affine arithmetic-based method and optimizing-scenarios method.

To address the uncertainty of renewable energy sources, the present work employs the reactive power optimization incorporating interval uncertainties (RPOIU) model for the transmission systems. In the RPOIU model, state variables, including load voltages, reactive power generation, and bus angles, are regarded as variables with interval values. Meanwhile, to account for the fluctuation of the load demand and the renewable energy sources in multiple periods of one day, a multi-time RPOIU is proposed. The model seeks to obtain a day-ahead optimal voltage control strategy for ensuring that interval state variables remain within their operating limit constraints in each period of one day, as well for maintaining a low level of daily real power losses. To solve the multi-time RPOIU model, we propose the interval sequential quadratic programming method (ISQPM), which employs a second-order interval Taylor expansion. In addition, an improved interval power flow calculation method i.e., the optimizing-scenarios method, is employed to obtain the accurate ranges of the interval variables, thus improving the convergence performance of the ISQPM. Three cases are tested by simulation to demonstrate the effectiveness, good applicability, and robustness of the proposed method, particularly in comparison to the previously proposed linear approximation method.

This letter proposes an efficient progressive polyhedral approximation (PA) method to tackle the high nonlinearity and nonconvexity of optimal electricity-water nexus (EWN) dispatch caused by hyperbolic nonlinear partial differential equations (HNPDEs). In this method, the HNPDE-constrained EWN dispatch model can be reformulated into a tractable mixed-integer linear programming (MILP) problem by tailored adaptive discretization and piecewise PA. Furthermore, a progressive approximation refinement technique is developed to dynamically strengthen the MILP for efficient convergence to a near-optimal solution. Comparative studies have validated the effectiveness of the proposed method in reducing decision-making time for the EWN dispatch.