Abstract
The differences between Buchholz's formula of apparent power and proposed formulation were demonstrated in the case of three-phase four-wire power system. It was shown that voltage integral from proposed formula of apparent power is the value of power losses in active resistances of power cable, which is due to load line-to-neutral voltages and short circuit mode of load. A new physical sense of apparent power was established, it is a geometric mean value of short-circuit power and power losses, caused by line currents. This definition of apparent power of three-phase power supply system is completely equivalent to definition standardized by IEEE. Conditions to achieve unit power factor and maximum efficiency of three-phase four-wire power system were established. The formula for determining efficiency of three-phase four-wire power system for unbalanced non-sinusoidal mode with a given load power factor and the known load factor has been derived. Computer simulation in MATLAB Simulink showed good agreement between the experimental data and the theoretical curves for efficiency both in the presence of the SAF, or without it.Ref. 8, Fig. 5, Таb. 1.
Highlights
The concept of Fryze's active current [1] as the vector of line currents with minimum mean-square norm, which provides the same load power at the given line-to-neutral voltages is widely applied to minimize the effective value of line current vector and associated power losses in power cable by using of shunt active filter (SAF) [2], [3]
Unlike (2), it is clearly visible in (5) the dependence of where R= rE + rN jjT is matrix of resistance losses in the power cable of three-phase four-wire power system that is symmetrical about the main diagonal; r is the resistance of each phase wire, rN is the resistance of the neutral wire; jT = 1 1 1 ; = uσ (t) r= R−1u(t) the apparent power and, power factor from the ratio of the resistances, giving by the coefficient σ in the presence of the vector's zero sequence components
The voltage integral from the expression (4) of apparent power is the value of power losses in active resistances of power cable, which is due to load line-toneutral voltages and short circuit mode of three-phase load:
Summary
Abstract—The differences between Buchholz's formula of apparent power and proposed formulation were demonstrated in the case of three-phase four-wire power system. It was shown that voltage integral from proposed formula of apparent power is the value of power losses in active resistances of power cable, which is due to load line-to-neutral voltages and short circuit mode of load. A new physical sense of apparent power was established, it is a geometric mean value of short-circuit power and power losses, caused by line currents. This definition of apparent power of three-phase power supply system is completely equivalent to definition standardized by IEEE. The formula for determining efficiency of three-phase four-wire power system for unbalanced non-sinusoidal mode with a given load power factor and the known load factor has been derived.
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