energía y telecomunicaciones. tema 2.1. circuitos de corriente alterna€¦ · circuitos de...
TRANSCRIPT
Tema 2.1. Circuitos de corriente alterna
Energía y Telecomunicaciones
Alberto Arroyo Gu;érrez Mario Mañana Canteli Raquel MarBnez Torre Jesús Mirapeix Serrano
Cándido Capellán Villacián
Departamento de Ingeniería Eléctrica y Energé5ca
Este tema se publica bajo Licencia: Crea5ve Commons BY-‐NC-‐SA 4.0
a a = 1!120
BCfGiIIj j = 1!90
LMPQR !SSuUUW JX !YZ !Z !!" !m# S/m$ U I%
+
+
+u
i
1
x(t) = X!2 cos(2&ft+ $0)
x(t) tXf$0 t = 0
X!2
x(t)
1f
f
xmedio xmedio = 1T
!T x(t)dt
xrms xrms ="
1T
!T x2(t)dt
xp xp = max{x(t)}xpp xpp = max{x(t)} "min{x(t)}
FC = xp
xrms
FF = xrmsxmedio
#
$%
$0
X"
X$0 = 0 % = 2&f
Urms Upico!2
R
u(t) = Ri(t)
U = RI
u(t)
+
i(t)
R
I U
L
u(t) = Ldi(t)
dt
U = j%LI
C
u(t) =1
C
#i(t)dt
u(t)
+
i(t)
LI
U
L
U =1
j%CI
u(t)
+
i(t)
C I
U
C
Z$
u(t) =!2U cos(%t)
i(t) =!2I cos(%t" $)
u(t)+
i(t)
Z
P
QS
$
Z
pi(t) = u(t)i(t) = 2UI cos(%t) cos(%t" $) = UI(cos(2%t" $) + cos($))
= UI(cos($)cos(2%t) + sin($) sin(2%t) + cos($))
= UI cos($)(1 + cos(2%t)) + UI sin($) sin(2%t)
= P (1 + cos(2%t)) +Q(sin(2%t))
P (1 + cos(2%t))Q sin(2%t)
P Q
P = UI cos($)
Q = UI sin($)
S
S =$P 2 +Q2
P Q S
$I!!!
S = U I"= U!0I!! = UI!! = UI cos($) + jUI sin($) = P + jQ
(%)
cos!cos" = 12 (cos(!+ ") + cos(!" "))
cos(!" ") = cos!cos" + sin!sin"
R S = U I"= U!0 I!0 = UI!0 &
P = UI;Q = 0
L S = U I"= U!0 I!90 = UI!90 &
P = 0;Q = UI
C S = U I"= U!0I!!90 = UI!!90 &
P = 0;Q = "UI
U
I % %
S =%N
i=1 Pi + j%N
i=1 Qi S1 = P1 + jQ1
S2 = P2 + jQ2
SN = PN + jQN
!" #$R1 R2
Ug
+
I R1 C
R2 L
P = 100+200 = 300 Q = 50"50 = 0 S =!3002 + 02 = 300
FPcos$
FP = cos$ =P
S=
P$P 2 +Q2
FPFP
FP
!" #$FP
FP FP = P!P 2+Q2
= 100#1002+502
= 0, 89
FPFP
S1
U+
I
C
S1 Red
FP
P Q
FPS1,abierto =P$
P 2 +Q2
S1 CQC Q > 0
QC < 0 FP
FPS1,cerrado =P$
P 2 + (Q +QC)2
Q$C FP FP $
FP $ =P$
P 2 + (Q +Q$C)
2
Q$C
Q$C = P
&1
FP !2" 1"Q
!" #$C
P Q % = 2&f = 2&50
FP $ C =100!1000
!112
!1
2"50·2302 = 6 µF
TE
TE
EACTIV A =
#
TP (t)dt
EREACTIV A =
#
TQ(t)dt
TE
TE
F
F = FPU + FEU
FPU
FEU
PotTPU
FPU = TPU · Pot
Pot
Pot
Pot
Pot
FEU ='
p
(Ep · TEUp)
Ep p
TEUp p
i(t) 45 e(t)R
e(t) = 230!2 cos(2&50t)
+
i(t) R 0, 1 H
10 µF
e(t) = 230!2 cos(2&50t)
+
i(t) 20 ! 20 mH
Zx 10 !
Zx C Zx FPFP
e(t) = 230!2 cos(2&50t)
+
i(t) 2 ! C
Zx
R1 R2 CC R1 = 10 ! C = 1 µF R2 = 10 !
E = 230 V+
i(t) R1
C R2
FPS1 C
S1 FP
E = 230 V+
i(t)
S1
C
20 !
0, 1 H
R = 286, 9 ! uR(t) = 230 cos(2&50t + 45 ) uL(t) = 25, 1 cos(2&50t + 135 ) uC(t) =255, 1 cos(2&50t" 45 )
Pg = 2407, 1 Qg = 756, 3 var S = 2523, 4
Zx = 6 + j8 ' 10!53,1 C = 157, 9 µF
UR1 = 115!0,09 UR2 = 114, 99!!0,09 IC = 0, 036!89,91
FP = 0, 54 (i) C = 72, 1 µF
TP = 16, 96 e E = 320 kWh TE = 36, 71 e Impuesto electricidad = 2, 74 eEquiposmedida = 1, 51 e Total = 67, 19 e
e
e
ee
e "