Balanced Delta-Delta Connection

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Questions and Answers

In a balanced delta-delta system, what characteristic defines the arrangement of the source and the load?

  • Both the source and the load are delta-connected. (correct)
  • The source is Y-connected while the load is delta-connected.
  • Both the source and the load are Y-connected.
  • The source is delta-connected while the load is Y-connected.

If the phase voltage of a delta-connected source is $V_p$, what are the line voltages $V_{ab}$, $V_{bc}$, and $V_{ca}$ assuming there are no line impedances?

  • $V_{ab} = V_p \angle 0^\circ$, $V_{bc} = V_p \angle -120^\circ$, $V_{ca} = V_p \angle +120^\circ$ (correct)
  • $V_{ab} = V_p \angle 30^\circ$, $V_{bc} = V_p \angle -90^\circ$, $V_{ca} = V_p \angle +150^\circ$
  • $V_{ab} = V_p \angle -30^\circ$, $V_{bc} = V_p \angle -150^\circ$, $V_{ca} = V_p \angle +90^\circ$
  • $V_{ab} = V_p \angle 60^\circ$, $V_{bc} = V_p \angle -60^\circ$, $V_{ca} = V_p \angle +180^\circ$

In a balanced delta-delta system, how are the line currents ($I_a$, $I_b$, $I_c$) related to the phase currents ($I_{AB}$, $I_{BC}$, $I_{CA}$)?

  • $I_a = I_{AB} - I_{CA}$, $I_b = I_{BC} - I_{AB}$, $I_c = I_{CA} - I_{BC}$
  • $I_a = I_{AB} + I_{CA}$, $I_b = I_{BC} + I_{AB}$, $I_c = I_{CA} + I_{BC}$
  • $I_a = I_{AB} / I_{CA}$, $I_b = I_{BC} / I_{AB}$, $I_c = I_{CA} / I_{BC}$
  • $I_a = I_{CA} - I_{AB}$, $I_b = I_{AB} - I_{BC}$, $I_c = I_{BC} - I_{CA}$ (correct)

What is the relationship between the line current ($I_L$) and the phase current ($I_p$) in a balanced delta-connected load?

<p>$I_L = \sqrt{3} I_p$ (C)</p> Signup and view all the answers

If a delta-connected load has an impedance of $Z_A$ per phase, what is the equivalent impedance ($Z_Y$) of the load if it were converted to a Y-configuration?

<p>$Z_Y = Z_A / 3$ (C)</p> Signup and view all the answers

A balanced delta-connected load has an impedance of $20 - j15 \Omega$ per phase. If the line voltage is $330\angle 0^\circ$ V, what is the magnitude of the phase current $I_{AB}$?

<p>13.2 A (B)</p> Signup and view all the answers

A balanced delta-connected load has an impedance of $20 - j15 \Omega$ per phase, and the phase current $I_{AB}$ is $13.2 \angle 36.87^\circ$ A. What is the phase angle of the line current $I_a$?

<p>6.87° (D)</p> Signup and view all the answers

A balanced delta-connected load has an impedance of $20 - j15 \Omega$ per phase. If the phase current $I_{AB}$ is $13.2 \angle 36.87^\circ$ A, what is the magnitude of the line current $I_a$?

<p>22.86 A (A)</p> Signup and view all the answers

In a balanced delta-delta system, a positive-sequence source supplies a balanced delta-connected load with an impedance per phase of $18 + j12 \Omega$. If the line current $I_a$ is $19.202 \angle 35^\circ$ A, what is the magnitude of the phase current $I_{AB}$?

<p>11.094 A (D)</p> Signup and view all the answers

In a balanced delta-delta system, a positive-sequence source supplies a balanced delta-connected load. If the impedance per phase of the load is $18 + j12 \Omega$ and the line current $I_a$ is $19.202 \angle 35^\circ$ A, what is the phase angle of the phase current $I_{AB}$?

<p>65° (A)</p> Signup and view all the answers

If the phase voltage is given as Vp/0°, what is the phase voltage Vcn in a balanced delta-connected source with positive sequence?

<p>Vp/+120° (B)</p> Signup and view all the answers

Which law is the basis for obtaining line currents from phase currents at nodes A, B, and C?

<p>Kirchhoff's Current Law (KCL) (D)</p> Signup and view all the answers

Given a balanced delta-delta system with a positive-sequence source and balanced delta-connected load, what is the phase relationship between the line current and corresponding phase current?

<p>Line current lags the phase current by 30°. (C)</p> Signup and view all the answers

A balanced delta-connected source supplies a balanced delta-connected load. The per phase impedance of the load is given by Z_A. To analyze the system by converting both load and source to their Y equivalents, what would be the per-phase impedance of the equivalent Y-connected load?

<p>Z_A/3 (D)</p> Signup and view all the answers

In a balanced delta-delta system, the balanced source has Va, Vb, and Vc, while the phase impedances are denoted ZA. What are the phase currents IAB, IBC, and ICA in relation to ZA?

<p>IAB=Vab/ZA, IBC=Vbc/ZA, ICA=Vca/ZA (B)</p> Signup and view all the answers

In a balanced delta-delta system, what does the term 'positive sequence' imply about the phase voltages?

<p>The phase voltages are equal in magnitude and are 120 degrees apart, with Vab leading Vbc and Vbc leading Vca. (C)</p> Signup and view all the answers

If the phase currents are IAB = 10∠0°, IBC = 10∠−120°, and ICA = 10∠120°, what would be the line current Ia?

<p>17.32∠30° (C)</p> Signup and view all the answers

A delta-delta three-phase system has a balanced load impedance of $Z_\Delta = 15 + j10 \Omega$ per phase. Determine the equivalent Y-connected impedance.

<p>$5 + j3.33 \Omega$ (D)</p> Signup and view all the answers

In a balanced delta-delta system, what is the line-to-line voltage across the load in terms of the phase voltages of the delta-connected source?

<p>The same as the phase voltage. (D)</p> Signup and view all the answers

In a balanced delta-delta circuit, if the phase current $I_{AB}$ has a magnitude of 20 amps, what is the approximate magnitude of the line current $I_a$?

<p>34.6 A (A)</p> Signup and view all the answers

A delta-connected load has a phase impedance of $Z = 30 + j40 \Omega$. If the line voltage is 480 V, what is the magnitude of the phase current?

<p>9.6 A (C)</p> Signup and view all the answers

Given a balanced delta-delta system, when is the delta-to-wye transformation most advantageous for simplifying calculations?

<p>When the source and load are both delta-connected and impedances are complex. (A)</p> Signup and view all the answers

In a three-phase delta-delta system, why is it important to ensure that both the source and the load are balanced?

<p>To ensure equal current distribution, prevent circulating currents, and maintain consistent power delivery. (D)</p> Signup and view all the answers

If each phase of a delta-connected generator produces a voltage of 120 V, what is most likely to be the line voltage of the generator?

<p>120 V (A)</p> Signup and view all the answers

What is the impact of having significant line impedances in a delta-delta system on the relationship between phase and line voltages?

<p>Line voltages will no longer be equal to the phase voltages due to voltage drops across the line impedances. (D)</p> Signup and view all the answers

If an impedance in a balanced delta-delta circuit is purely reactive, what can be expected?

<p>The current and voltage will be out of phase. (A)</p> Signup and view all the answers

What conditions are necessary for a delta-delta system to be considered 'balanced'?

<p>Equal voltage magnitudes with 120-degree phase separation, and equal phase impedances. (C)</p> Signup and view all the answers

How does a 'positive sequence' differ from a 'negative sequence' in a three-phase delta-delta system?

<p>In ‘positive sequence’, voltage peaks in order ABC; in ‘negative sequence’, they peak in order CBA. (A)</p> Signup and view all the answers

If a delta-delta system experiences a fault within one of the phase impedances, what immediate effect would that have with respect to line currents?

<p>Causes significant imbalance in line currents with potential overload. (C)</p> Signup and view all the answers

In a delta-delta power system how is power balance generally reflected in the system's phases regarding current, voltage, and impedance?

<p>Equal magnitude voltage and current, and identical impedance in each phase. (C)</p> Signup and view all the answers

Why must a delta-delta system be carefully monitored for imbalances even if designed to be balanced?

<p>Because even in balanced systems, all configurations are prone to imbalances due to factors like component aging or uneven loads causing circulating currents and reducing efficiency. (A)</p> Signup and view all the answers

Within a properly operating balanced delta-delta system, describe how each of the three phases contribute to the overall power delivery.

<p>Each phase contributes equally to the overall power delivery. (C)</p> Signup and view all the answers

If a load in a delta-delta system requires more power than available, which of the following steps would likely be taken to mitigate any issues due to overloading.

<p>Balance the load by redistributing it among the phases or by using additional circuits. (A)</p> Signup and view all the answers

In a delta-delta system protected with circuit breakers, how do these breakers typically respond to an overload condition?

<p>Circuit breakers act quickly to interrupt the flow of electricity, protecting sensitive components within the system. (C)</p> Signup and view all the answers

A balanced delta-connected load of $Z = 10 + j0 \Omega$ per phase is connected to a balanced delta-connected source with a line voltage of 100V. Calculate the magnitude of the DELTA phase current.

<p>10 A (C)</p> Signup and view all the answers

A balanced delta-connected load of $Z = 10 + j0 \Omega$ per phase is connected to a balanced delta-connected source with a line voltage of 100V. Calculate the magnitude of the LINE current.

<p>$\sqrt{3} * 10$ A (A)</p> Signup and view all the answers

A balanced delta-connected load with $Z = 10 + j0 \Omega$ per phase has DELTA phase currents $I_{AB} = 10A, I_{BC} = -5 -j8.66A, I_{CA} = -5 + j8.66A$. What is the magnitude of $I_A$.?

<p>$\sqrt{3}*10$ (C)</p> Signup and view all the answers

A balanced 3-phase delta connected load having Z = 10 Ohms is supplied by a balanced Y connected source having 100V line to neutral with no line impedance. What do you expect the LINE CURRENT value to be?

<p>sqrt(3)*10 (D)</p> Signup and view all the answers

Flashcards

Balanced Delta-Delta System

A system where both the source and load are delta-connected and balanced.

Line Voltages

Voltages measured directly across two lines in a three-phase system.

Line Currents

Currents flowing through the lines connecting the source to the load.

Delta-Y Conversion

Zy = Za/3. It is a method to simplify delta connections.

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Phase Current Calculation

VAB/ZA. Used to calculate phase currents in a delta-delta system.

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Line Current Relationship

IL = √3Ip. The line current always lags the corresponding phase current by 30°.

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Study Notes

Balanced Delta-Delta Connection

  • A balanced Delta-Delta (Δ-Δ) system has both the balanced source and balanced load connected in a delta configuration.
  • The goal is to determine the phase and line currents.
  • Assuming a positive sequence, the phase voltages for a delta-connected source are expressed as:
    • Vab = Vp/0°
    • Vbn = Vp/-120°
    • Vcn = Vp/+120°
  • The line voltages are the same as the phase voltages, assuming no line impedances.
  • Phase voltages of the delta-connected source equal the voltages across the impedances, represented as:
    • Vab = VAB
    • Vbc = VBC
    • Vca = VCA
  • Phase currents can be determined as:
    • IAB = VAB/ZA
    • IBC = VBC/ZA
    • ICA = VCA/ZA
  • Line currents are found using Kirchhoff's Current Law (KCL) at nodes A, B, and C, as:
    • Ia = IAB - ICA
    • Ib = IBC - IAB
    • Ic = ICA - IBC
  • IL = √3Ip
  • An alternative way to analyze the Δ-Δ circuit is to convert both the source and the load to their Y equivalents, where Zy = ZA/3

Example 1

  • Balanced Δ-connected load has an impedance 20 – j15 Ω
  • Connected to a Δ-connected, positive-sequence generator having Vab = 330/0° V.
  • The load impedance per phase is computed as ZL = 20 – j15 = 25/-36.87° Ω
  • With VAB = Vab = 330/0°, phase currents are calculated:
    • IAB = (330/0°) / (25/-36.87°) = 13.2/36.87° A
    • IBC = IAB/-120° = 13.2/-83.13° A
    • ICA = IAB/+120° = 13.2/156.87° A
  • For a delta load, the line current always lags the corresponding phase current by 30° and has a magnitude √3 times that of the phase current.
  • Therefore, the line currents are:
    • Ia = IAB√3/-30° = (13.2/36.87°)(√3/-30°) = 22.86/6.87° A
    • Ib = Ia/-120° = 22.86/-113.13° A
    • Ic = Ia/+120° = 22.86/126.87° A

Practice Problem

  • A positive-sequence, balanced Δ-connected source supplies a balanced Δ-connected load.
  • The impedance per phase of the load is 18 + j12 Ω
  • IAB = 19.202/35° A
  • Find IAB and VAB
  • Answer: 11.094/65° A, 240/98.69° V

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