Lecture #11 EGR 272 – Circuit Theory II Read: Chapter 11 in Electric Circuits, 6th Edition by Nilsson Chapter 11 - Three Phase (3) Circuits So far we have only considered single phase (1) circuits. Transmission of power Power is transmitted using AC since voltage levels are easily stepped up for transmission and down for customers through the use of transformers. As voltage increases, current decreases, so line losses (I2R losses) are reduced. AC voltages are generated using 3 phase voltages (three voltages that are separated in phase by 120°). Businesses and industry commonly use 3 phase voltages. The 3 phases are split up so that a residential neighborhood uses only one of the 3 phases. A single phase voltage of 240V is provided to a house along with 120V formed using a center tap transformer (illustrate below).

Lecture #11 EGR 272 – Circuit Theory II Advantages of 3-phase circuits: more efficient (smaller I2R losses) less vibration in machinery smaller conductors Polyphase circuits AC voltages can be generated using various numbers of phases. 3 phase is the most common 6 and 12 phase are sometimes seen

Lecture #11 EGR 272 – Circuit Theory II Single-phase (1  ) and 3-phase (3 ) generators 3- phase generator Single-phase generator (3 sets of windings on the rotor, where each are physically staggered by 120º) + V - (one set of windings on the rotor) + Van - + Vbn - + Vcn - Generator coil representation Generator coil representation + V - + Van - + Vbn - + Vcn - Waveforms (abc phase sequence) : Waveform t V t Van Vbn Vcn

Lecture #11 EGR 272 – Circuit Theory II TCC Engineering students touring the Dominion Virginia Power Nuclear Power Station in Surry, VA One of the 800 MW 3-phase steam turbine generators is shown on the right. Nuclear energy is used to heat water and create steam to power the generators.

Lecture #11 EGR 272 – Circuit Theory II TCC Engineering students touring the Dominion Virginia Power Nuclear Power Station in Surry, VA Huge transformers are used to increase the voltage to 500,000 V before it leaves the power plant. Increases the voltage reduces the current, resulting in lower line losses (I2R) during transmission.

Lecture #11 EGR 272 – Circuit Theory II Three small transformers are mounted on the wall in the old electronics lab (Lynnhaven Building, Room 144). Each transformer carries a separate phase. The outputs of the transformers were used for 3-phase experiments.

Lecture #11 EGR 272 – Circuit Theory II 3 transformers on a pole carry 3-phase power along Indian River Road in Virginia Beach 1 transformer on a pole carries 1 single phase into a nearby neighborhood in Virginia Beach

Lecture #11 EGR 272 – Circuit Theory II Phase sequences The three phases may be arranged in two possible phase sequences: 1) abc (or positive) phase sequence 2) acb (or negative) phase sequence t Van Vbn Vcn t Van Vcn Vbn

Lecture #11 EGR 272 – Circuit Theory II Phase sequences The two possible phase sequences are sometimes represented by phasor diagrams as shown below. Note: A practical illustration of the effect of phase sequence is that if a 3 motor is connected with an abc phase sequence it will turn in one direction and if it is connected with an acb phase sequence it will turn in the other direction.

Lecture #11 EGR 272 – Circuit Theory II Generator Connections There are two basic types of generator connections: Wye (Y) generator Delta () generator

Lecture #11 EGR 272 – Circuit Theory II The wye and delta generators shown on the previous page might also be represented using voltage sources, as shown in the PSPICE schematics below. Wye Generator Delta Generator

Lecture #11 EGR 272 – Circuit Theory II Balanced versus unbalanced generators Balanced generators have the same magnitude for each phase and exactly 120o of phase shift between each phase. Systems with balanced generators are easier to analyze. Example: For each case shown below, is the generator balanced? What is the phase sequence? Circle the correct responses.

Lecture #11 EGR 272 – Circuit Theory II 3 Y generator Define the line voltages Vab , Vbc , and Vca . Show how to calculate line voltages in general using KVL. Show that for a balanced Y generator:

Lecture #11 EGR 272 – Circuit Theory II 3  generator Show that the line voltages are equal to the generator phase voltages. In general, for a Y generator:

Lecture #11 EGR 272 – Circuit Theory II Load connections There are two common ways to connect the three phase loads: 1) Wye (Y) connection 2) Delta (D) connection Wye (Y) Load: Note: A wye load is balanced if ZAN = ZBN = ZCN. Discussion: When would loads be balanced?

Lecture #11 EGR 272 – Circuit Theory II Delta Load: Note: A delta load is balanced if ZAB = ZBC = ZCA.

3-Phase Generator Load Lecture #11 EGR 272 – Circuit Theory II Generator-load configurations There are several possible generator and load configurations, including: 1) Y-Y a) 4-wire b) 3-wire 2) Y-D 3) D -D 4) D -Y 3-Phase Generator Load 4-wire Y-Y system Y-Generator Y-Load

Lecture #11 EGR 272 – Circuit Theory II Example: A 4-wire Y-Y system has a balanced generator with Van = 480 V and a positive phase sequence.

Lecture #11 EGR 272 – Circuit Theory II Y- D system: Note that the Y- D system is significantly more difficult to analyze that the Y-Y system.

Lecture #11 EGR 272 – Circuit Theory II Example: Determine all three line currents in a Y -  system that has a balanced generator with Van = 240 V and a negative phase sequence.