Since the appearance impedances of a counterbalanced star- or delta-connected amount accommodate according currents, the appearance ability is one-third of the absolute power. As a definition, the voltage beyond the amount impedance and the accepted in the impedance can be acclimated to compute the ability per phase.
Let’s accept that the bend amid the appearance voltage and the appearance accepted is θ, which is according to the bend of the impedance. Considering the amount configurations accustomed in Fig. 3-22, the appearance ability and the absolute ability can be estimated easily.
Figure 3-22. Per-phase admiral in (a) a delta-connected amount and (b) a star-connected load.
In the case of Fig. 3-22a, the absolute alive ability is according to three times the ability of one phase.
Since the band accepted in the counterbalanced delta-connected loads, if this blueprint is commissioned into blueprint 3.51, the absolute alive amount becomes
In Fig. 3-22b, however, the impedances accommodate the band currents Iline (= appearance current, Iphase) and the appearance voltages ). Therefore, the appearance alive ability and the absolute alive ability are
If the accord amid the appearance voltage and the band voltage () is used, the absolute alive ability becomes identical to the blueprint developed in blueprint 3.52. This agency that the absolute ability in any counterbalanced three-phase amount (Δ- or Y-connected) is accustomed by blueprint 3.52.
Similarly, the absolute acknowledging and the absolute credible ability in the three-phase counterbalanced ac circuits can be accustomed by
In the three-phase ability systems, one, two, or three wattmeters can be acclimated to admeasurement the absolute power. A wattmeter may be advised to be a voltmeter and an ammeter accumulated in the aforementioned box, which has a bend proportional to VrmsIrms cos θ, area θ is the bend amid the voltage and current. Hence, a wattmeter has two voltage and two accepted terminals, which accept or − polarity signs. Three ability altitude methods utilizing the wattmeters are declared next, and are activated to the balanced three-phase ac load.
This adjustment can be acclimated in a three-phase three-wire counterbalanced or asymmetric amount arrangement that may be affiliated Δ or Y. To perform the measurement, two wattmeters are affiliated as credible in Fig. 3-23.
Figure 3-23. Two-wattmeter adjustment in star- or delta-connected load.
In the counterbalanced loads, the sum of the two wattmeter readings gives the absolute power. This can be accurate in a star-connected amount mathematically application the ability account of anniversary beat as
If the aberration of the readings is computed,
which is times the absolute three-phase acknowledging power. This agency that the two-wattmeter adjustment can additionally announce the absolute reactive ability in the three-phase endless and additionally the ability agency (see Fig. 3-24).
Figure 3-24. Three-phase voltage phasors acclimated in the two-wattmeter method.
This adjustment is acclimated in a three-phase four-wire counterbalanced or asymmetric load. The access are fabricated with one beat in each band as credible in Fig. 3-25. In this configuration, the absolute alive ability supplied to the amount is according to the sum of the three wattmeter readings.
Figure 3-25. The wattmeter access in the three-phase four-wire loads.
This adjustment is acceptable alone in three-phase four-wire counterbalanced loads. The affiliation of the wattmeter is agnate to the drawing accustomed in Fig. 3-25. The absolute ability is according to three times the account of alone one wattmeter that is affiliated amid one appearance and the neutral terminal.
The cold of this area is to accept the admiral and the ability altitude techniques associated with the three-phase ac circuits. Fig. 3-26 illustrates the advanced console of the VI called Three appearance ability measurements.vi.
Figure 3-26. The advanced console and abrupt user adviser of Three appearance ability measurements.vi.
Before belief this VI, accomplish abiding that you abstraction and accept the ability abstraction presented in Area 3.2.2. Open and run the custom-written VI called Three appearance ability measurements.vi in the Affiliate 3 folder, and investigate the afterward questions.
A counterbalanced three-phase, three-wire star-connected amount is affiliated to a three-phase supply. The band voltage is 400 V. The amount comprises an impedance of 100 j100 Ω per phase. Set these ambit and baddest the acceptable ambit to actuate the absolute active, reactive, and apparent ability by application the VI provided.
Assume that the amount in catechism 1 is a four-wire circuit. Use three ability altitude methods and affirm your allegation manually.
Three 10 μF capacitors are affiliated in brilliant (Y) beyond a 2300 V (rms, band voltage), 60 Hz line. Calculate the band current, the active power, the acknowledging power, and the credible ability by application the VI.
A three-phase boiler dissipates 15 kW back affiliated to a 208 V, three-phase line. Actuate the amount of anniversary resistor if they are affiliated as star.
An automated bulb draws 600 kVA from a 2.4 kV band at a ability agency of 0.8 lagging. What is the agnate line-to-neutral impedance of the plant?
An electric motor accepting a ability agency 0.82 draws a accepted of 25 A from a 600 V three-phase ac supply. Find the alive power supplied to the motor.
Each appearance of a delta-connected amount comprises a resistor of 50 Ω and a capacitor of 50 μF in series. The three-phase amount is affiliated to a 440 V (rms, band voltage) and 50 Hz three-phase brilliant (Y)-connected supply. Calculate the appearance and band currents, the ability factor, the absolute alive power, and absolute credible power. Observe the phasor diagrams application the VI accustomed in the antecedent section, 3phase phasors.vi.
Hint: First, transform the delta-connected amount to a star-connected agnate (see Area 2.5). Then accomplish the ability calculations.
Answers: 5.46 A (rms), 9.46 A (rms), 0.62, 4480 W, 7240 VA
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