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Questions and Answers
In a balanced delta-delta system, what characteristic defines the arrangement of the source and the load?
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?
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 ($I_{AB}$, $I_{BC}$, $I_{CA}$)?
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?
What is the relationship between the line current ($I_L$) and the phase current ($I_p$) in a balanced delta-connected load?
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?
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?
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 $I_{AB}$?
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 $I_{AB}$?
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 $I_a$?
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 $I_a$?
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 $I_a$?
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 $I_a$?
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 $I_{AB}$?
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 $I_{AB}$?
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 $I_{AB}$?
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 $I_{AB}$?
If the phase voltage is given as Vp/0°, what is the phase voltage Vcn in a balanced delta-connected source with positive sequence?
If the phase voltage is given as Vp/0°, what is the phase voltage Vcn in a balanced delta-connected source with positive sequence?
Which law is the basis for obtaining line currents from phase currents at nodes A, B, and C?
Which law is the basis for obtaining line currents from phase currents at nodes A, B, and C?
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?
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?
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?
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?
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?
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?
In a balanced delta-delta system, what does the term 'positive sequence' imply about the phase voltages?
In a balanced delta-delta system, what does the term 'positive sequence' imply about the phase voltages?
If the phase currents are IAB = 10∠0°, IBC = 10∠−120°, and ICA = 10∠120°, what would be the line current Ia?
If the phase currents are IAB = 10∠0°, IBC = 10∠−120°, and ICA = 10∠120°, what would be the line current Ia?
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.
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.
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?
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?
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 $I_a$?
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 $I_a$?
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?
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?
Given a balanced delta-delta system, when is the delta-to-wye transformation most advantageous for simplifying calculations?
Given a balanced delta-delta system, when is the delta-to-wye transformation most advantageous for simplifying calculations?
In a three-phase delta-delta system, why is it important to ensure that both the source and the load are balanced?
In a three-phase delta-delta system, why is it important to ensure that both the source and the load are balanced?
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?
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?
What is the impact of having significant line impedances in a delta-delta system on the relationship between phase and line voltages?
What is the impact of having significant line impedances in a delta-delta system on the relationship between phase and line voltages?
If an impedance in a balanced delta-delta circuit is purely reactive, what can be expected?
If an impedance in a balanced delta-delta circuit is purely reactive, what can be expected?
What conditions are necessary for a delta-delta system to be considered 'balanced'?
What conditions are necessary for a delta-delta system to be considered 'balanced'?
How does a 'positive sequence' differ from a 'negative sequence' in a three-phase delta-delta system?
How does a 'positive sequence' differ from a 'negative sequence' in a three-phase delta-delta system?
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?
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?
In a delta-delta power system how is power balance generally reflected in the system's phases regarding current, voltage, and impedance?
In a delta-delta power system how is power balance generally reflected in the system's phases regarding current, voltage, and impedance?
Why must a delta-delta system be carefully monitored for imbalances even if designed to be balanced?
Why must a delta-delta system be carefully monitored for imbalances even if designed to be balanced?
Within a properly operating balanced delta-delta system, describe how each of the three phases contribute to the overall power delivery.
Within a properly operating balanced delta-delta system, describe how each of the three phases contribute to the overall power delivery.
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.
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.
In a delta-delta system protected with circuit breakers, how do these breakers typically respond to an overload condition?
In a delta-delta system protected with circuit breakers, how do these breakers typically respond to an overload condition?
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.
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.
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.
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.
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 $I_A$.?
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 $I_A$.?
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?
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?
Flashcards
Balanced Delta-Delta System
Balanced Delta-Delta System
A system where both the source and load are delta-connected and balanced.
Line Voltages
Line Voltages
Voltages measured directly across two lines in a three-phase system.
Line Currents
Line Currents
Currents flowing through the lines connecting the source to the load.
Delta-Y Conversion
Delta-Y Conversion
Zy = Za/3. It is a method to simplify delta connections.
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Phase Current Calculation
Phase Current Calculation
VAB/ZA. Used to calculate phase currents in a delta-delta system.
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Line Current Relationship
Line Current Relationship
IL = √3Ip. The line current always lags the corresponding phase current by 30°.
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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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