In this paper, a mechanical model of a transformer–bushing with an inerter isolation system (IIS) is established. An IIS is composed of an inerter element, a damping element, and a spring element connected in parallel between the same two terminals. Vibration control equations and frequency response functions are also established. The influence of parameters on IIS, including inerter–mass ratio, damping ratio, and frequency ratio, was studied. In the extremum condition that represents the most efficient parameter set of inerter–mass ratio and damping ratio for relative displacement response ratio, an optimal design method was developed by exploiting a performance demand. Finally, the seismic response of the transformer–bushing with IIS was carried out to verify the isolation performance of IIS. The research shows that the equivalent mass coefficient and damping coefficient of IIS can be amplified by an inerter element and the inerter–mass ratio and damping ratio are reduced simultaneously under the conditions of meeting the performance demand after parameter optimization. Meanwhile, the parameter optimization design method proved to be effective for meeting the target demand of the relative displacement response of the bushing and tank, while base shear force and isolation displacement were reduced simultaneously. Based on the results from a response history analysis under ground motion records, IISs can significantly suppress the resonance response of a structure and the continuous vibration response in the stable state. The peak displacement can be reduced by 50% compared with a traditional isolation system.

In this paper, parameter analyses of a tuned inerter damper (TID) are carried out based on the displacement mitigation ratio. The optimal design of TID based on the closed-form solution method is carried out and compared with the fixed-point method. Meanwhile, applicable conditions of two methods are discussed in wider range of values of objective function under different inherent damping ratios. Finally, seismic responses of SDOF system with TID are carried out, which verifies the feasibility of the closed-form solution optimization method. Compared with the fixed-point method, the inherent damping ratio of the original structure is considered in the closed-form solution method, and the optimal damping ratio of a TID is smaller than that of the fixed-point method under same displacement mitigation ratio. The parameters’ combination of a TID designed by the fixed-point method obtains a vibration mitigation effect with a larger damping ratio by cooperating with the deformation enhancement effect of the inerter, which may make the vibration mitigation effect of the TID lower than that of the VD in structures with large inherent damping ratios. However, the deformation enhancement effect on the damping element of the inerter can be fully used by using the closed-form solution method. Better applicability and robustness are shown in closed-form solution method. Under the same displacement mitigation ratio, the damping ratio of a TID obtained by using the closed-form solution method is about one tenth of that obtained by using the fixed-point method, which can realize the lightweight design of the TID.

In this study, a single-degree-of-freedom (SDOF) model with cable inerter viscous damper (CIVD) is established, and the vibration control equations and frequency response functions are established. Then, the influence of parameters, including inertia mass ratio, additional damping ratio, and stiffness ratio, is studied. Finally, the dynamic time history analysis of SDOF with CIVD under earthquake and fluctuating wind load is carried out to verify the damping performance of CIVD. The research shows that the additional mass and damping of CIVD can be amplified hundreds of times through the rotation, so as to realize the lightweight and high efficiency of the damper and make up for the engineering defects of the traditional TMD system. Meanwhile, when designing CIVD, the inertia mass ratio and additional damping ratio should be reduced as much as possible under the condition of meeting the target damping ratio. The CIVD can significantly suppress the resonance response of the structure and the continuous vibration response in the stable state. The peak displacement can be reduced by 3050. Installing the cable and inerter element can control only the structural vibration, but it cannot reduce the amplitude in the steady state. The CID can control the inertial force output of the original structure, but the rotating speed of the inerter element is high, and the shaking speed of the original structure is fast. Therefore, in order to control the acceleration, velocity, and displacement of the original structure at the same time, we must add the appropriate inerter, additional damping, and additional stiffness.

Transformer vibration and noise has become a prominent problem in power grid construction and operation. Firstly, on the basis of expounding the vibration mechanism of iron core and winding, the transmission path of vibration and noise of transformer is analyzed. Secondly, it is pointed out that it is not cost-effective to control transformer vibration and noise only from the selection of core and winding materials, manufacturing process and structural optimization. It is necessary to start from the transmission path of transformer sound and vibration, and adopt auxiliary vibration reduction and noise reduction measures such as vibration isolation of the body to reduce the transmission of vibration of the body to the oil tank wall, foundation and adjacent structures. Then, the design method of oil immersed power transformer body vibration isolation is discussed, and the relevant parameters such as frequency ratio, damping ratio and the arrangement of vibration isolation support are proposed. The reasonable vibration isolation design of transformer body can achieve remarkable vibration isolation effect and the vibration isolation efficiency can reach more than 96%. Finally, the vertical design stiffness of 81 kinds of oil immersed power transformer vibration isolation layers with 4 voltage levels of 10 kV, 35 kV, 110 kV and 220 kV are calculated. Taking a typical 110 kV transformer as an example, the corresponding vibration isolation design scheme is proposed. The research provides a good reference for the vibration isolation design of transformer body in the future.

In DC microgrid (DC-MG), the loads connected with converters under strict control are considered as CPLs (constant power loads). When the voltage of CPLs decreases, the current increases and the negative impedance characteristic of CPLs cause instability easily. Fortunately, appropriate control for energy storage units could improve the system stability. However, most traditional control methods for bidirectional DC-DC power converters (BDC) connected with battery storage units do not quantitatively consider the stability influences of control parameters. This paper quantitatively analyzes the stability influence of the BDC current-mode control parameters and the negative impact of CPLs and derives the control parameter determination method for BDC interfaced storage systems. Large signal stability constraints are obtained in terms of mixed potential function. According to the constraints, the large signal stability is improved when the BDC control parameter k_p increases, while the stability is degraded when the power of CPLs increases. The control parameter determination method is very effective and convenient to apply, and the appropriate parameter k_p for BDC is determined. The regions of asymptotic stability (RAS) identify that the proposed control parameter determination method could improve the system stability effectively. The determination method is fully verified by the simulation and experimental results.

In this paper, the mechanical model of grotto–eave system with cable inerter viscous damper (CIVD) is established, and the vibration control equations are established. Firstly, the stochastic response is carried out, and the optimization design of design parameters of CIVD is carried out for the grotto–eave systems with different connection types. Finally, the vibration mitigation control performance of CIVD under different seismic inputs is analyzed. The research shows that in the optimal design of CIVD, the inerter–mass ratio and damping ratio should be reduced as much as possible to improve the feasibility of the application of CIVD in cultural relics protection engineering under the condition of meeting the target damping ratio. The demand-based optimal method can minimize the cost by enhancing damping element deformation in a small damping ratio, while ensuring that the value of displacement index of grotto–eave system can be reached. Hence, the deformation and damping force of CIVD will increase simultaneously due to the efficient tuning and damping amplification of CIVD. CIVD can enlarge the apparent mass through rotation and damping force through enhancement deformation. Hence, compared with other conventional dampers (such as viscous damper), optimal CIVD has lower damping ratio under the same demand index of grotto–eave system. It can be realized that the lightweight and high efficiency of the damper, and can be applied to the vibration mitigation and reinforcement of the grotto–eave system.