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electrical_engineering_2:polyphase_networks [2024/06/18 02:38] – [Excercises] mexleadminelectrical_engineering_2:polyphase_networks [2024/11/17 10:30] (aktuell) – [7.2.2 Three-Phase System] mexleadmin
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   * Simple three-phase machines can be used for generation.   * Simple three-phase machines can be used for generation.
-  * Rotary field machines (e.g. synchronous motors or induction motors) can also be simply connected to a load, converting the electrical energy into mechanical energy.+  * Rotary field machines (e.g., synchronous or induction motors) can also be simply connected to a load, converting electrical energy into mechanical energy.
   * When a symmetrical load can be assumed, the energy flow is constant in time.   * When a symmetrical load can be assumed, the energy flow is constant in time.
   * For energy transport, the voltage can be up-transformed and thus the AC current, as well as the associated power loss (= waste heat), can be reduced.   * For energy transport, the voltage can be up-transformed and thus the AC current, as well as the associated power loss (= waste heat), can be reduced.
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 === Three-phase generator === === Three-phase generator ===
  
-  * The windings of a three-phase generator are called $\rm U$, $\rm V$, $\rm W$; the winding connections are correspondingly called: $\rm U1$, $\rm U2$, $\rm V1$, $\rm V2$, $\rm W1$, $\rm W2$ (see <imgref imageNo10>). \\ <WRAP> +  * The windings of a three-phase generator are called $\rm U$, $\rm V$, $\rm W$. \\ Often they are also colour-coded as red, yellow and blue - and consecutively sometimes also called $\rm R$, $\rm Y$, $\rm B$. 
 +  * The winding connections are correspondingly called: $\rm U1$, $\rm U2$, $\rm V1$, $\rm V2$, $\rm W1$, $\rm W2$ (see <imgref imageNo10>). \\ <WRAP> 
 <imgcaption imageNo10 | Motor Terminal></imgcaption> {{drawio>Motorterminal.svg}} </WRAP> <imgcaption imageNo10 | Motor Terminal></imgcaption> {{drawio>Motorterminal.svg}} </WRAP>
-  * The typical **winding connections**  in a three-phase generator are called **Delta connection** (for ring connection) and **Wye connection** (for star connection). This winding connection can simply be changed by reconnecting the motor terminal. In <imgref imageNo11> the two types of winding connections are shown. For the Wye connection, is often the star configuration shown, and for the Delta connection the ring configuration. For the Wye connection, it is also possible to have the star point on a separate terminal. <WRAP> +  * The typical **winding connections**  in a three-phase generator are called **Delta connection** (for ring connection) and **Wye connection** (for star connection). This winding connection can simply be changed by reconnecting the motor terminal. In <imgref imageNo11> the two types of winding connections are shown. For the Wye connection, it is often the star configuration shown, and for the Delta connection the ring configuration. For the Wye connection, having the star point on a separate terminal is also possible. <WRAP> 
 <imgcaption imageNo11 | Motor Terminal Setup for the two Connections></imgcaption> {{drawio>MotorterminalConnections.svg}} </WRAP> <imgcaption imageNo11 | Motor Terminal Setup for the two Connections></imgcaption> {{drawio>MotorterminalConnections.svg}} </WRAP>
   * The **phase voltages**  are given by: <WRAP>    * The **phase voltages**  are given by: <WRAP> 
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 A passive component is fed by a sinusoidal AC voltage with the RMS value $U=230~\rm V$ and $f=50.0~\rm Hz$. The RMS current on this component is $I=5.00~\rm A$ with a phase angle of $\varphi=+60°$. A passive component is fed by a sinusoidal AC voltage with the RMS value $U=230~\rm V$ and $f=50.0~\rm Hz$. The RMS current on this component is $I=5.00~\rm A$ with a phase angle of $\varphi=+60°$.
  
-1. Draw the equivalent circuits based on a series and on a parallel circuit. \\+1. Draw the equivalent circuits based on a series and a parallel circuit. \\
  
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 A magnetic coil shows at a frequency of $f=50.0 {~\rm Hz}$ the voltage of $U=115{~\rm V}$ and the current $I=2.60{~\rm A}$ with a power factor of $\cos \varphi = 0.30$ A magnetic coil shows at a frequency of $f=50.0 {~\rm Hz}$ the voltage of $U=115{~\rm V}$ and the current $I=2.60{~\rm A}$ with a power factor of $\cos \varphi = 0.30$
  
-  - Calculate the real power, the reactive power, and the apparent power .+  - Calculate the real power, the reactive power, and the apparent power.
   - Draw the equivalent parallel circuit. Calculate the active and reactive part of the current.   - Draw the equivalent parallel circuit. Calculate the active and reactive part of the current.
   - Draw the equivalent series circuit. Calculate the ohmic and inductive impedance and the value of the inductivity.   - Draw the equivalent series circuit. Calculate the ohmic and inductive impedance and the value of the inductivity.
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-#@TaskTitle_HTML@#7.2.3 Motor on 3-Phase System II#@TaskText_HTML@#+#@TaskTitle_HTML@#7.2.3 Heater on 3-Phase System#@TaskText_HTML@# 
 + 
 +A three-phase heater with given resistors is connected to the $230~\rm V$/$400~\rm V$ three-phase system. The heater shows purely ohmic behavior and can be configured in wye or delta configuration. \\ 
 + 
 +  - The heater is configured in a delta configuration and provides a constant heating power of $6 ~\rm kW$. 
 +    - Calculate the resistor value of a single string in the heater 
 +    - Calculate the RMS values of the string currents and phase currents. 
 +  - The heater with the same resistors as in 1. is now configured in a wye configuration.  
 +    - Calculate the RMS values of the string currents and phase currents. 
 +    - Compare the heating power in delta configuration (1.) and wye configuration (2.)  
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 + 
 +#@TaskTitle_HTML@#7.2.4 Motor on 3-Phase System II#@TaskText_HTML@#
  
 A three-phase motor is connected to a three-phase system with a phase voltage of $400 ~\rm V$. The phase current is $16 ~\rm A$ and the power factor $0.9$. \\ A three-phase motor is connected to a three-phase system with a phase voltage of $400 ~\rm V$. The phase current is $16 ~\rm A$ and the power factor $0.9$. \\
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-#@TaskTitle_HTML@#7.2.4 Motor on 3-Phase System III#@TaskText_HTML@#+#@TaskTitle_HTML@#7.2.5 Motor on 3-Phase System III#@TaskText_HTML@#
  
 A symmetrical and balanced three-phase motor of a production line shall be configured in a star configuration and provide a power of $17~\rm kW$ with a power factor of $0.75$. The voltage on a single string is measured to be $135 ~\rm V$. \\ A symmetrical and balanced three-phase motor of a production line shall be configured in a star configuration and provide a power of $17~\rm kW$ with a power factor of $0.75$. The voltage on a single string is measured to be $135 ~\rm V$. \\