Lecture 91 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

Lecture 92 Three-Phase Circuits In three-phase circuits the 3 voltages sources are 120° apart Polyphase generation and transmission of electricity is more advantageous and economical (1) three-phase instantaneous power is constant over time (2) single-phase line losses are 50% greater than three-phase losses (for the same load power, voltage, pf), i.e., P Single =3/2×P Three

Lecture 93 Balanced System A balanced system is one in which the 3 sinusoidal voltages have the same magnitude and frequency, and each is 120° out-of-phase with the other two

Lecture 94 Three-Phase Voltages V an +–+– +–+– V bn +–+– V cn n c b a Balanced If: V an =V rms  0°V bn =V rms  -120°V cn =V rms  -240°

Lecture 95 MATLAB Exercise Let’s create and plot balanced 3-phase voltages EDU» t=0:0.0005:0.04; EDU» va=120*sqrt(2)*cos(377*t); EDU» vb=120*sqrt(2)*cos(377*t-2*pi/3); EDU» vc=120*sqrt(2)*cos(377*t-4*pi/3); EDU» plot(t,va,'b:',t,vb,'g--',t,vc,'r') EDU» legend(’va',’vb',’vc') Don’t exit MATLAB, we shall return

Lecture 96 Balanced Circuit A balanced three-phase circuit is one in which the loads are such that the currents produced by the voltages are also balanced

Lecture 97 MATLAB Exercise Let’s now create and plot some corresponding balanced 3-phase currents EDU» figure; EDU» ia=10*sqrt(2)*cos(377*t-pi/8); EDU» ib=10*sqrt(2)*cos(377*t-pi/8-2*pi/3); EDU» ic=10*sqrt(2)*cos(377*t-pi/8-4*pi/3); EDU» plot(t,ia,'c:',t,ib,'k--',t,ic,'m')

Lecture 98 Three-Phase Instantaneous Power Recall that the instantaneous power is for one phase is p(t) = i(t) v(t) The total instantaneous power for three phases is –the instantaneous power is a constant over time!

Lecture 99 MATLAB Exercise Let’s now compute the individual and total instantaneous powers, and plot them EDU» figure; EDU» pa=va.*ia; EDU» pb=vb.*ib; EDU» pc=vc.*ic; EDU» pt=pa+pb+pc; EDU» plot(t,pa,'b:',t,pb,'g--',t,pc,'r',t,pt,'k-.')

Lecture 910 Three-Phase Connections Standard notation specifies the phase sequence as abc (called positive phase sequence) where V an =V p  0°V bn =V p  -120°V cn =V p  -240° V bn =V an  -120° V cn =V an  -240° –V bn lags V an by 120° –where V p is the phase voltage which is the magnitude of the phasor voltage from the neutral to any line The balanced voltage set means that V an + V bn + V cn = 0 [Book Error]

Lecture 911 Wye (Y) Connected Load ZYZY a ZYZY b ZYZY c Load ZYZY ZYZY ZYZY a b c n n

Lecture 912 Delta (  ) Connected Load ZZ ZZ ZZ a c b Load ZZ ZZ ZZ a b c