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This paper introduces a new method of estimating the variation interval and the expected value of optimal economic operation cost for the energy hub (EH) model considering load and renewable energy uncertainties in the residential district. Firstly, renewable energy and load uncertainties are defined as uncertain sets of historical data. Due to dispatch factors, the traditional EH model is non-linear and difficult to calculate and analyze. In this paper, a multi-step modeling method is developed for the breakdown of a complex EH model (CEH) into several simple EH (SEH) models and variable substitutions in each SEH, to eliminate the non-linearity of CEH. The upper and lower bound of the operating costs are then obtained based on the duality theorem and the expected value is calculated by expected value model. Finally, the case study in Beijing residential district is carried out to confirm the efficiency of the proposed method.

Voltage sag is one of the most common power quality disturbances in industry, which causes huge inrush current in the windings of induction motors, and adversely impacts the motor's secure operation. For better understanding of the operation and protection of induction motors, there is a need for a detailed research of the transient characteristics of induction motors during sag events. In this paper, we first proposed a novel 2-D multi-slice field-circuit-motion coupling time-stepping finite element method (2-D multi-slice FCM coupling T-S FEM) for calculating the transient performance of the induction motor with skewed rotor bars. In the proposed method, the equations of field, circuit, and motion are expressed in a nodal matrix and coupled together. Based on this method, we have analyzed the electromagnetic properties of a 5.5-kW induction motor with skewed rotor bars under symmetrical voltage sag conditions. Then, the influences of voltage sag's sag magnitude, phase-angle jump, and initial phase angle on the stator inrush peak currents of the 5.5 kW and a 55-kW induction motors is studied. Finally, the proposed method is compared with 3-D FEM, the traditional 2-D multi-slice FEM and the measured data. The results show that the proposed method can reduce the computation time significantly with high precision.