Equipo4___Tarea_5___Power_Calculations_in_a_Three_Phase_System (1)

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Benemérita Universidad Autónoma de Puebla
Facultad de Ciencias de la Electrónica
Licenciatura en Ingeniería Mecatrónica
Tarea 5. Power Calculations in a Three-Phase System
Materia: Sistemas Electrónicos de Potencia
Docente: Gerardo Mino Aguilar
NRC: 60122
Integrantes del equipo: Matrículas
Alarcón Castillo Karen Araceli 202116808
Arrasquito Lima Francisco Andrés 202107394
Barragán Suárez Carlos 202107622
Bueno de la Rosa Carmen Guadalupe 202120529
Soriano Sánchez Diego Armando 202161538
Periodo: Primavera 2025
Índice
1. Active Power (P) 2
1.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Reactive Power (Q) 2
2.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3. Apparent Power (S) 3
3.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4. Instantaneous Power (p) 3
4.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
5. Average Power 4
5.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
6. RMS Power 5
6.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7. Power Factor (PF) 5
7.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8. Total Harmonic Distortion (THDi and THDv) 6
8.1. Exercise: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1
1. Active Power (P)
1.1. Exercise:
Calculate the active power for a three-phase system with line voltage VLL = 127V , line
current IL = 10A, and a power factor cosϕ = 0,9.
Solution
P = V Icosϕ = (127V )(10A)(0,9)
P = 1, 143W
Answer: P=1,143W
2. Reactive Power (Q)
2.1. Exercise:
Calculate the reactive power for the same system.
Solution
Using
sin2ϕ+ cos2ϕ = 1
⇒ sinϕ =
√︁
1− cos2ϕ =
√︁
0,19
Therefore sinϕ = ±0,436
Then
Q = V Isinϕ
Q = (127V )(10A)(±0,436)
Q = ±553,72V AR
Answer:Q = ±553,72VAR
2
3. Apparent Power (S)
3.1. Exercise:
Calculate the apparent power.
Solution
S = V Icosϕ = (127V )(10A)
S = 1270V A
or
S =
√︁
P 2 +Q2 =
√︁
11432 + 553,722
S = 127,060V A ≈ 1270V A
Answer: S = 1270VA
4. Instantaneous Power (p)
4.1. Exercise:
For a single-phase system, the instantaneous voltage and current are given by v(t) =
Vmsin(ωt) and i(t) = Imsin(ωt+ ϕ). Calculate the instantaneous power.
Solution
p(t) = v(t) · i(t) = Vmsin(ωt) · Imsin(ωt+ ϕ)
Using the trigonometric identity
sinA · sinB =
1
2
[cos(A−B)− cos(A+B)]
Applying this
p(t) = VmIm · 1
2
[cos(ωt− (ωt+ ϕ))− cos(ωt+ (ωt+ ϕ))]
3
Simplifying
p(t) =
VmIm
2
[cos(−ϕ)− cos(2ωt+ ϕ)]
Since cos(−ϕ) = cos(ϕ) -para, the final expression is:
p(t) =
VmIm
2
[cos(ϕ)− cos(2ωt+ ϕ)]
Answer: p(t) = VmIm
2
[cos(ϕ)− cos(2ωt+ ϕ)]
5. Average Power
5.1. Exercise:
Calculate the average power for the above system.
Solution
The average (active) power in a single-phase system is calculated as:
Pavg =
VmIm
2
cos(ϕ)
Since Vrms =
Vm√
2
and Irms =
Im√
2
, we can rewrite the formula as:
Pavg = Vrms · Irms · cosϕ
Answer: Pavg = Vrms · Irms · cosϕ
4
6. RMS Power
6.1. Exercise:
Calculate the RMS value of the power.
Solution
Using the formula to approximate the power in RMS
PRMS = VRMS · IRMS
Since Vrms =
Vm√
2
and Irms =
Im√
2
, we can rewrite the formula as:
PRMS =
Vm√
2
· Im√
2
Answer: PRMS = Vm√
2
· Im√
2
7. Power Factor (PF)
7.1. Exercise:
Calculate the power factor given the active and apparent powers.
Solution
Using the formula provided in class, the power factor is defined as:
PF =
P
S
Answer: PF = P
S
5
8. Total Harmonic Distortion (THDi and THDv)
8.1. Exercise:
Calculate the THDi and THDv if the fundamental current is I1 = 10A and the second
harmonic is I2 = 1A, and the voltage distortion is similar.
Solution
The THD for the current (THDi) is calculated as:
THDi =
√︁∑︁∞
h=2I
2
h
I1
Since only the second harmonic is considered (I2 = 1A):
THDi =
√︁
I22
I1
=
1
10
= 0,1
For THDv, if the distortion is similar, then: THDv = 0,1
Answer: THDi = 0,1 y THDv = 0,1
6
Highlight
	Active Power (P)
	Exercise:
	Reactive Power (Q)
	Exercise:
	Apparent Power (S)
	Exercise:
	Instantaneous Power (p)
	Exercise:
	Average Power
	Exercise:
	RMS Power
	Exercise:
	Power Factor (PF)
	Exercise:
	Total Harmonic Distortion (THDi and THDv)
	Exercise: