Cooperation of a Non-Linear Receiver with a Three-Phase Power Grid

Abstract

This article presents an analysis of electrical parameters in a three-phase circuit characterized by the generation of harmonics. The Currents Physical Components (CPC) power theory for three-phase circuits were used. Relationships for three-wire circuits were used, and mathematical relationships were determined to enable decomposition into those components that depend on the direction of energy flow and the reasons for their creation. A calculation example using the previously determined dependencies was presented, and the results of the calculations were discussed. When mathematical analyses are required in circuits with non-linear receivers, and in particular, when there is a cooperation of several such receivers with a common power grid, the calculation concept presented is important. The generation of identical harmonic orders by several receivers causes a disturbance in the direction of energy flow in the power grid. For this reason, the case of a non-linear receiver generating harmonics of orders that has existed before in the power grid seems very interesting. Determining the value of individual powers can be used to estimate the impact of individual receivers on the quality of electricity.

Description of a three-phase, four-wire system with a nonlinear receiver and an asymmetric voltage source using CPC power theory

“…From (19), the value of the equivalent conductance is Ge = 4.65 S, while from (48) the active power PD forces the flow of current iaD with an effective value equal 859.5 A.…”

“…With the adopted notation, the set of N harmonics was divided into ND and NC sets [19]. When the active power Pn for the n th harmonic is positive, it should be assumed that it comes from the D system (Fig.…”

“…Correct performance of power compensation [11], [12], [19], [20], as well as determining the energy parameters of three-phase circuits depend on the adopted definition of apparent power. Building the power theory on several foundations of apparent power causes the obtained results to be contradictory even in the case of sinusoidal waveforms.…”

Budeanu’s Distortion Power Components Based on CPC Theory in Three-Phase Four-Wire Systems Supplied by Symmetrical Nonsinusoidal Voltage Waveforms

“…Initially, the author of CPC considered both single-phase systems with sinusoidal and nonsinusoidal voltages [2,[13][14][15]. Subsequently, the theory progressed to encompass three-phase three-wire (3-p 3-w) systems [14][15][16][17][18][19] and three-phase four-wire (3-p 4-w) systems [20][21][22][23][24][25][26][27][28][29][30]. The evolution of the theory involved describing each of these three-phase systems for both symmetrical supply [2,[13][14][15]21,22,[28][29][30] and asymmetrical supply [18][19][20][23][24][25][26][27].…”

“…Subsequently, the theory progressed to encompass three-phase three-wire (3-p 3-w) systems [14][15][16][17][18][19] and three-phase four-wire (3-p 4-w) systems [20][21][22][23][24][25][26][27][28][29][30]. The evolution of the theory involved describing each of these three-phase systems for both symmetrical supply [2,[13][14][15]21,22,[28][29][30] and asymmetrical supply [18][19][20][23][24][25][26][27]. Moreover, all these systems have detailed descriptions covering ideal reactance compensation [15,16,18,19,22,25,26], as well as the minimization of reactance compensation [20,24,[31][32][33].…”