In this article, a new mathematical model of a major hysteresis loop and a simple procedure for the formation of first-order and higher-order reversal curves are proposed. The applicability of the model has been tested by comparison with measured results, obtained with electrical steel and ferrite cores, and simulation results obtained with the Preisach model. Very good agreement has been found between simulated and measured major and minor hysteresis loops, as well as first-order and higher-order reversal curves.

Liquid-level control in tanks is widely used in various industrial sectors. Due to problems arising from the case that the liquid level is above or below the recommended, the process of its control is of great significance. The proportional integral differential (PID) controller is one of the most widely used controllers in applications that require accuracy and optimal automatic control. In this paper, single and coupled ship fuel tank systems are discussed. In addition, mathematical models and their linearization using two different approaches are presented. The two control approaches are used to maintain the specified liquid level in tanks. The first is based on the design of standard PID controllers, with the application of the Ziegler–Nichols, Takahashi tuning, and Auto-tuning methods. The second approach, proposed by the authors, is based on the application of the Dahlin algorithm. The simple modification of the Dahlin controller, which can avoid the “ringing” of the control signal, is suggested in the paper. Moreover, the lower limit of the decrease in the desired time constant, which ensures the desired behavior of the system, is determined. The comparisons provided for different performance indexes show the advantages of the modified Dahlin algorithm approach compared to the standard PID controllers. Furthermore, the comparison with the literature-known approaches is realized.

The aim of this paper is to present the results of measurements for the magnetic hysteresis loop and the specific power loss of the electrical steel obtained with the toroidal samples of various dimensions. All samples have been made of the same material. Numerous measurements have been performed after the annealing of the samples. The measurements have been performed with control of the sinusoidal shape of the secondary voltage. Differences between the results of measurements have been analyzed. Change in the measured results, e.g. the shape of the hysteresis loop or the specific power loss has been correlated to the dimensions of the sample.

Analysis of error in measuring electric energy and maximum power within direct and half-indirect measurement system at the voltage of 0.4kV is presented in the paper. The analysis involved all the elements of the measurement system, i.e. calibration and testing of the transformer-operated and direct digital energy meters and measuring current transformers. This equipment was also used for measurements in the transformer substation aiming at error analysis at measurements made under the real conditions. The results obtained show significant negative measurement error introduced by the energy meters under overload conditions. Energy meters have lower values of both the consumed electric energy and maximum power in this operating mode, which can be interpreted as a loss.

Electric field and potential distribution in the surroundings of cube electrodes are numerically determined using Equivalent Electrodes Method.