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8.2 Star-Balanced Load

Now on, we analyze a three-phase voltage system with three star-connected loads (Fig. 8.1). Taking into account that it is a balanced nature system.

Diagram of a three-phase circuit with three horizontal lines labeled 1, 2, and 3. Vertical arrows indicate voltages V12, V23, V31, and V30. Three vertical components labeled Z1, Z2, and Z3 are connected to the lines, with currents I1, I2, and I3 flowing through them. A current labeled In flows downward from the junction of these components.

Fig. 8.1 Star balanced load. Source own elaboration

Then, we write for each of the loads:

$Z_{1} ∠ φ_{1} = Z_{2} ∠ φ_{2} = Z_{3} ∠ φ_{3}$

Applying Ohm's law to each of these loads, we find the currents flowing through each phase:

$I_{1} ⇀= \frac{U _{10} ⇀}{Z _{1} ∠ φ _{1}} (8.2)$

$I_{2} ⇀= \frac{U _{20} ⇀}{Z _{2} ∠ φ _{2}} (8.3)$

$I_{3} ⇀= \frac{U _{30} ⇀}{Z _{3} ∠ φ _{3}} (8.4)$

Since the voltage is 120° out of phase, the system of currents is also 120° out of phase with each other, and has an angle φ regarding to each of their corresponding voltage. Since the impedance in the line and the applied voltage are equal, so does the current.

$I_{1} = I_{2} = I_{3} = I_{L} (8.5)$

As we see in the vector diagram Fig. 8.4, it satisfies the following condition:

$I_{1} ⇀ + I_{2} ⇀ + I_{3} ⇀= I_{N} ⇀= 0 (8.6)$

Question Under these circumstances, is it possible to eliminate the neutral conductor? If this is the case, it is possible to create an artificial neutral at the most common point of the star-connected loads, which makes it possible to maintain a single voltage between the phases and the neutral without using the neutral conductor. It is important to keep in mind that this is only possible in balanced load scenarios.

练习题

In a balanced star-connected three-phase load, which condition must be satisfied by the impedances?

Z_{1} ∠ φ_{1} = Z_{2} ∠ φ_{2} = Z_{3} ∠ φ_{3}

Z_{1} = Z_{2} = Z_{3}

but

φ_{1} \neq = φ_{2} \neq = φ_{3}

C. Only the magnitudes

∣ Z_{1} ∣, ∣ Z_{2} ∣, ∣ Z_{3} ∣

must be equal

D. The impedances can be different if the voltages compensate for the difference

In a balanced star-connected load, if the phase voltages are 120° apart, what is the phase relationship between the phase currents?

A. The phase currents are in phase with each other

B. The phase currents are also 120° out of phase with each other

C. The phase currents have random phase relationships

D. The phase currents are 60° out of phase with each other

Under what condition can the neutral conductor be safely eliminated in a star-connected three-phase system?

A. When the load is unbalanced and currents differ

B. Only when all three phases have different impedances

C. When the load is balanced

D. When the neutral current exceeds the phase currents

Which of the following statements are true for a balanced star-connected three-phase load?

A. All three impedances have equal magnitude and phase angle

B. The phase currents are equal in magnitude

C. The phase currents are 120° out of phase with each other

D. The neutral current equals zero

E. The neutral current equals the sum of phase current magnitudes

In a balanced star-connected load, the vector sum of all three phase currents equals zero.

An artificial neutral point can be created at the common junction of star-connected loads even when the load is unbalanced.

In a balanced three-phase star-connected system, each phase current lags or leads its corresponding phase voltage by the same angle $φ$ .

In a balanced star-connected load, the phase currents have equal magnitudes expressed as: $I_1 = I_2 = I_3 = ___$

The neutral current in a balanced star-connected load is given by the equation: $\vec{I_1} + \vec{I_2} + \vec{I_3} = \vec{I_N} = ___$

Explain why the neutral conductor can be eliminated in a balanced star-connected three-phase load, and describe what happens at the common junction point of the three loads.

In a balanced star-connected three-phase load, if each phase impedance is $Z = 10∠30° Ω$ and the phase voltage is $U_{P} = 230 V$ , which statement correctly describes the relationship between line current and phase current?

A. The line current is

3

times the phase current, and all three line currents have different magnitudes

B. The line current equals the phase current, and all three line currents have equal magnitudes

C. The line current equals the phase current, but the three line currents have different magnitudes due to the 120° phase difference

D. The line current is

3

times the phase current, and all three line currents have equal magnitudes

A three-phase motor connected in star configuration requires a neutral conductor to maintain proper operation because the phase currents are 120° out of phase with each other.

Which of the following conditions must be satisfied for a neutral conductor to be safely eliminated in a three-phase star-connected system?

A. All three phase impedances must be equal (

Z_{1} = Z_{2} = Z_{3}

)

B. The three-phase currents must be 120° out of phase with each other

C. The system must be a balanced load

D. The line voltage must equal the phase voltage

In a star-connected three-phase system, the line current equals the _ current. When the load is balanced, the neutral current equals _, which allows the neutral conductor to be eliminated.

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8.2 Star-Balanced Load