This paper proposes a low-carbon operation model for an energy hub (EH) that combines the distributionally robust optimization (DRO) method with the Stackelberg game. Firstly, a bilevel single-leader-multi-follower Stackelberg game model is presented where the EH is the leader while users and electric vehicles (EVs) are regarded as two followers. Then, the Kullback-Leibler (KL) divergence-based DRO model is developed to deal with the uncertainty of renewable generation (RG) in the EH. Besides, Karush–Kuhn–Tucker (KKT) conditions, strong duality theory, and big- M approach are combined to transform the bilevel model into a single-level model. The reformulated single-level operation model is incorporated into the KL-based DRO approach. Furthermore, since the crafted column and constraint generation (C&CG) algorithm can prevent possible numerical problems caused by the exponential function and accelerate the solution speed, the crafted C&CG algorithm with linearization for the upper-level slave problem is proposed to iteratively solve the KL-based DRO integrated with Stackelberg game. Finally, numerical case studies are conducted with all simulation results confirming the effectiveness of the proposed model and method.

As the increasing complexity and uncertainty of integrated energy systems, the cooperative interaction under uncertainty between the energy hub (EH) and multi-energy users has become crucial for the efficient operation of energy systems. This paper proposes a unified collaborative and interactive framework to optimize operations between the EH and multi-energy users under uncertainty. Firstly, in the horizontal dimension, the stochastic distributionally robust chance-constrained (S-DRCC) optimization method with the Wasserstein metric is proposed to hedge against the uncertainty of EH considering the multiple scenarios and moment information of uncertain variables. Then in the vertical dimension, a bi-level Stackelberg game model is developed for EH and users to facilitate the collaborative interaction for multi-agents. Furthermore, several efficient methods are leveraged to reformulate the originally intractable framework into a tractable mixed-integer linear programming (MILP) model that can be directly solved using commercial solvers. Finally, the effectiveness of the proposed model and method are demonstrated by numerical case studies and corresponding simulation results.

The inner winding of the power transformer is subjected to uniform compressive stress in the radial direction during the short circuit, which makes circular radial stability a crucial component of reliability. The radial stability evaluation system currently needs more state characteristic judgment quantity considering the manufacturing deviations(MD) and assembly gaps. Thus, there is a significant deviation in the transformer design, which seriously endangers the operation safety of the power system. This paper proposes an improved radial buckling analysis method (IRBAM) to investigate the circular radial stability of inner winding. The IRBAM is implemented by defining two characteristic parameters: equivalent flexibility and MD. Besides, the relative change ratio of impedance (RCRI) is proposed as the buckling judgment for ending each short-circuit test. The destructive short-circuit tested transformer is designed with the rated power of 50 MVA and the high-voltage (HV) rated voltage of 110 kV. Then, 73 cumulative short-circuit tests are performed until impedance exceeds the permissible value based on the judgment. Finally, it is verified that IRBAM can effectively match the winding failure modes by comparing the buckling phenomena and calculation results. Further, the IRBAM can provide a reference for similar designs and verification with more minor deviations.

This study analyzes and evaluates the feasibility of a harmonic suppression traction transformer (HSTT) for harmonic reduction in railway systems. This new type of transformer can improve the power quality of railway systems by preventing high-frequency harmonic currents from injecting into the traction grid. As the physical size of available space in high-speed trains is strictly limited, low space-occupying filtering techniques are needed. Therefore, an HSTT with integrated filtering inductors (IFIs) capable of being implemented in regular trains is proposed. Taking advantage of the HSTT, a specially constructed inductive-capacitive-inductive (LCL)-type filter is used for harmonic suppression instead of a regular LCL-type filter. The proposed filter is composed of an integrated inductor, leakage inductor of the traction transformer, and an external filter capacitor. In this paper, we analyze the topology of the proposed system, construct a mathematical model to reveal the magnetic decoupling theory of IFIs, and discuss the design and calculation procedures of the HSTT with IFIs. The field circuit coupling simulation of the HSTT with IFIs is performed to validate the effectiveness of the proposed system. Finally, the practical operation based on a 10 kVA prototype shows that the proposed scheme can not only suppress the high-order frequency harmonics but also decrease the installed space of filter devices.

With the increasing penetration of distributed photovoltaic (PV) in distribution network, time-varying PV generation may result in severe voltage problems. Utilizing the reactive power capacity of PV inverters to regulate voltage offers a viable solution to mitigate the limitations of traditional reactive power compensators. This paper proposes an online accelerated dual ascent method (ADAM) based voltage control strategy for a distribution network with rich PV. The voltage control problem is initially formulated as a convex quadratic optimization problem to maintain the permissible voltage profiles of the PV nodes with the operation constraint on voltage and reactive power output capacity. Then, the ADAM is proposed to solve the optimization problem in a distribution manner. The proposed method can achieve a fast convergence speed by adding the accelerated algorithm to the traditional dual ascent method (DAM). In the distributed algorithm, each agent only collects neighbor information without global communication, thus, the complexity of computation and communication can be alleviated effectively. Moreover, the control strategy leverages real-time voltage measurements to respond promptly to typical daily voltage variations—such as midday voltage rise and nighttime voltage drop. The efficiency and superiority of the proposed method are validated through simulations on the IEEE 123-bus test system with high penetration of PV and a representative rural distribution network in China.