In the present work, a procedure for the estimation of internal damping in a cracked rotor system is described. The internal (or rotating) damping is one of the important rotor system parameters and it contributes to the instability of the system above its critical speed. A rotor with a crack during fatigue loading has rubbing action between the two crack faces, which contributes to the internal damping. Hence, internal damping estimation also can be an indicator of the presence of a crack. A cracked rotor system with an offset disc, which incorporates the rotary and translatory of inertia and gyroscopic effect of the disc is considered. The transverse crack is modeled based on the switching crack assumption, which gives multiple harmonics excitation to the rotor system. Moreover, due to the crack asymmetry, the multiple harmonic excitations leads to the forward and backward whirls in the rotor orbit. Based on equations of motions derived in the frequency domain (full spectrum), an estimation procedure is evolved to identify the internal and external damping, the additive crack stiffness and unbalance in the rotor system. Numerically, the identification procedure is tested using noisy responses and bias errors in system parameters.

In the rotor system, depending upon the ratio of rotating (internal) damping and stationary (external) damping, above the critical speed may develop instability regions. The crack adds to the rotating damping due to the rubbing action between two faces of a breathing crack. Therefore, there is a need to estimate the rotating damping and other system parameters based on experimental investigation. This paper deals with a physical model based an experimental identification of the rotating and stationary damping, unbalance, and crack additive stiffness in a cracked rotor system. The model of the breathing crack is considered as of a switching force function, which gives an excitation in multiple harmonics and leads to rotor whirls in the forward and backward directions. According to the rotor system model considered, equations of motion have been derived, and it is converted into the frequency domain for developing the estimation equation. To validate the methodology in an experimental setup, the measured time domain responses are converted into frequency domain and are utilized in the developed identification algorithm to estimate the rotor parameters. The identified parameters through the experimental data are used in the analytical rotor model to generate responses and to compare them with experimental responses.

The single-phase voltage loss is a common fault. Once the voltage-loss failure occurs, the amount of electrical energy will not be measured, but it is to be calculated so as to protect the interest of the power supplier. Two automatic calculation methods, the power substitution and the voltage substitution, are introduced in this paper. Considering the lack of quantitative analysis of the calculation error of the voltage substitution method, the grid traversal method and MATLAB tool are applied to solve the problem. The theoretical analysis indicates that the calculation error is closely related to the voltage unbalance factor and the power factor, and the maximum calculation error is about 6% when the power system operates normally. To verify the theoretical analysis, two three-phase electrical energy metering devices have been developed, and verification tests have been carried out in both the lab and field conditions. The lab testing results are consistent with the theoretical ones, and the field testing results show that the calculation errors are generally below 0.2%, that is correct in most cases.