Chapter 12 Three-Phase Circuit Analysis

A three phase generator has three coils each represent a phase Va N S N S N S N S N S N S N S N S Vb I b Vb I a Va Vc Vc I c

Three-phase system

Why do we use 3-phase systems? Three-phase system produces rotating magnetic field. Three-phase motors can start without the need for extra equipment. For the same physical size, a three-phase generator produces more power than a single phase generator. Three-phase lines transmit more power. Three-phase lines are more reliable. In distribution circuit, you can operate the system with one missing phase.

Y-Connection-Source

Phase voltage V V a n b V c V V V n c a b cn an bn cn bn an Reference Transmission Line Generator V an Reference a n a b V bn c b Van Vbn Vcn V cn V bn V an n

Line-to-line voltage V ca bc ab n c b a Van Vbn Vcn

Reference V ab ca n bn cn an bc -V The other line to line voltages

Main Conclusions Line-to-line voltage is greater than phase voltage by Line-to-line voltage leads phase voltage by

Example v v Let for a balanced three phase system Reference 30 Calculate the line-to-line voltages v an The other voltages can be computed by the balanced system relationship

Y-Connected System I I I I I I I I I a a Z n n Z Z c c V V V Line current Transmission Line Source Load I Phase current a a a + + I Z V I a an a I n b n V V Z Z cn bn + I c + b c + b I + I I b c c b I c

Three Phase System

Y-Connection For balanced system

V cn I c q n V an Reference I b q V bn I a q

Neutral Current of Balanced Load I c For balanced system I a I b

Main Conclusions for Y-Connected Load Line-to-line voltage is greater than phase voltage by Line-to-line voltage leads phase voltage by Line current equals phase current

Example: For the three phase system shown , find The load currents of each phase The neutral current The magnitude of the line to line voltage Ia a b c b c Ib Ic

The load currents of each phase The other currents can be computed by the balanced system relationship The neutral current The magnitude of the line to line voltage

Delta () Connection: Load Ia a _ Ica + Iab I bc ab n V ca Reference q _ Ib + b _ c + Ic Ibc

I ca V ab Reference n q I ab I bc 300 I a - Ica

Main Conclusions for Delta-Connected Load Line-to-line voltage of the source is equal to phase voltage (across load). The line current (coming from the source) is greater than phase current (of the load) by Line current lags phase current by

Example Calculate the phase currents of the load a Iab Ia Ica c b b c Ib Ibc Ic

a b c Ia Ic Van Ib Z

Power of 3-phase circuits Iphase Vphase For Single phase IMPORTANT  is the angle between phase voltage and phase current. Use voltage as a reference For 3-phase

Real Power in Y Circuit a b c Ia Ib Ic Van Vcn Vbn

Reactive Power in Y Circuit b c Ia Ib Ic Va Vc Vb

Real Power in Delta Circuit b c Ia Ib Ic Iab Ica Ibc + _

Reactive Power in Delta Circuit b c Ia Ib Ic Iab Ica Ibc + _

Two-meter method for measuring three-phase power Three Phase Power Measurement Two-meter method for measuring three-phase power