Determination of the extremes of power and losses in a separate phase of the electrical network

Сформулированы и решены задачи поиска экстремумов мощности в зависимости от характера тока при заданной форме напряжения и абсолютного экстремума функции мощности в зависимости от соотношения гармонических составляющих. Получены соотношения для коэффициентов мощности и потерь на активном сопротивлении проводов в линиях электропередач в отдельной фазе электрической сети. Соотношения позволяют рассчитывать, как мгновенные, так и интегральные оценки качества электропотребления.To assess the quality of power consumption, the processes of power transfer in a separate phase in the most general case for non-sinusoidal voltage and non-sinusoidal current are considered. The problem of searching for power extremes is determined and solved depending on the nature of the current for a given voltage form, as well as determining the absolute extremum of the power function as a function of the ratio of the harmonic components. The calculated ratios for the calculation of the power and loss factors for the active resistance of wires in power lines in a separate phase of the electrical network are given. Ratios allow us to calculate both instantaneous and integral estimates of the quality of power consumption, taking into account such consumer properties as symmetry, linearity, the presence of reactivity. Analysis of the results shows that the maximum power occurs when the ratio of the current amplitudes is equal to the ratio of the voltage amplitudes. Regardless of the nature of the voltage, the possible maximum power for a fixed loss level is transferred to the load if it is a constant active resistance. In this case, the maximum possible power is equal to the product of the actual values of voltage and current. Thus, the main source of increased power losses in electrical networks is the reactivity of the consumer. The resulting relationships can be successfully applied in real devices for monitoring the quality of power consumption, as well as meters