Lesson 15: Polyphase Alternating Current
Recommended Post : 【Circuit Theory】 Circuit Theory Table of Contents
1. Overview
2. Voltage and Current of Balanced Three-Phase Power Circuits
4. Power in Three-Phase Circuits
5. Symmetrical n-Phase Circuits
1. Overview
⑴ Polyphase AC System
① Several mechanical powers with the same frequency but different phases coexist in the same circuit
② Advantage 1: High efficiency of generation
③ Advantage 2: Generation and transmission of high voltage
④ Advantage 3: Generated power remains constant regardless of time
⑤ Advantage 4: Low risk of failure
⑵ Symmetrical Polyphase System
① When n polyphase powers have the same magnitude and phase differences between them are equal
② Antonym : Asymmetrical Polyphase System
⑶ Balanced Polyphase System
① When the sum of instantaneous powers of each phase is constant
② Unbalanced Polyphase System
⑷ 3-Phase Generator : A generator with three windings spaced 120° apart on the rotor
Figure. 1. Configuration of a 3-Phase Generator
2. Voltage and Current of Balanced Three-Phase Power Circuits
⑴ Voltage and Current in Y Power Circuits
⑵ Voltage and Current in Δ Power Circuits
##3. Y-Δ Connection of Loads
⑴ Let’s denote the resistances close to terminals a, b, c in a Y circuit as Ra, Rb, Rc, respectively.
⑵ Let’s denote the resistances between terminals a-b, b-c, c-a in a Δ circuit as R1, R2, R3, respectively.
⑶ Total composite resistance between terminals a-b, b-c, c-a
⑷ Y → Δ Equivalence Transformation : Rarely used. Holds for impedance as well.
⑸ Δ → Y Equivalence Transformation : Frequently used. Holds for impedance as well.
4. Power in Three-Phase Circuits
5. Symmetrical n-Phase Circuits
⑴ Formation of Phasors
① Line voltage
② Line current = Phase current
③ Phase relationship : Line voltage leads phase current, and its magnitude is as follows.
⑵ Imaginary Configuration
① Line voltage = Imaginary voltage
② Line current
③ Phase relationship : Line current lags phase current, and its magnitude is as follows.
⑶ Rotating System
① Switching the phase sequence of any two coils in 3-phase AC changes the direction of the rotating system
② Rotating system’s angular velocity is a constant angular velocity ω
③ Symmetrical n-phase AC forms a circular rotating system, asymmetrical n-phase AC forms an elliptical rotating system
④ Power supplied to a symmetrical balanced load in a balanced polyphase AC circuit remains constant regardless of time
⑷ n-Phase Power
① Formulation
② 3-voltage method
Figure. 2. 3-voltage method
③ 3-current method
Figure. 3. 3-current method
④ 2-power method : Method to measure the power of a 3-phase load using two power meters (* Note: Denotes complex conjugate)
Figure. 4. 2-power method
By drawing vector diagrams, the following facts can be observed
6. Three-Phase V-Connection
⑴ Voltage and Current in V-Connection
① In the case of a fault in one power source in a Δ-connected 3-phase power system, switching to a V-connection can supply 3-phase voltage to the load without any issue.
⑵ V-Connection, Y-Connection, Δ-Connection
① Y-Connection ○ Line voltage
○ Line current
○ Output
② Δ-Connection
○ Line voltage
○ Line current
○ Output
③ V-Connection
○ Line voltage
○ Line current
○ Output
⑶ Output Ratio
① Output ratio = V-Connection output ÷ 3-phase output = 1 ÷ √3
⑷ Utilization Factor
① Utilization factor = 3-phase output ÷ Equipment capacity = √3 / 2
② When changing from Δ-Connection to V-Connection, the output decrease is 1/ √3.
7. Symmetrical Coordinate System
⑴ Unbalanced Voltage
① Unbalanced voltage = Zero-sequence voltage + Positive-sequence voltage + Negative-sequence voltage
○ Unbalance factor = Negative-sequence ÷ Positive-sequence × 100 (%)
② Zero-sequence : Components with the same magnitude and in-phase as a neutral component, exist on the central axis of the grounding line
③ Positive-sequence : Voltage with a phase difference of 120˚ between phases a, b, c
④ Negative-sequence : Voltage with a phase difference of 120˚ between phases a, c, b
⑤ Formulation : Using the principle of superposition, taking voltage as an example.
○ Conversely,
⑵ Basic Equation for AC Generators
① Zero-sequence
② Positive-sequence
③ Negative-sequence
⑶ Interpretation of Intertwined Short Circuit : Using Symmetrical Coordinates
① Using Positive Impedance and Negative Impedance
Input : 2016.01.20 18:55
Revised : 2018.01.06 12:49