electrical technology et 201
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ELECTRICAL TECHNOLOGY ET 201. Explain and calculate average power, apparent power, reactive power Calculate the total P, Q and S and sketch the power triangle. Power in AC Circuit. Power is distributed into the resistance and reactance in AC circuit. - PowerPoint PPT PresentationTRANSCRIPT
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Explain and calculate average power, apparent power, reactive power
Calculate the total P, Q and S and sketch the power triangle.
ELECTRICAL TECHNOLOGY ET 201
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• Power is distributed into the resistance and reactance in AC circuit.
• The power delivered to a load at any instant is defined by the product of the applied voltage and the resulting current:
• Since v and i are sinusoidal quantities
Power in AC Circuit
vip
tVv m sin
tIi m sin
3
The chosen v and i include all possibilities because
• If the load is purely resistive: = 0°
• If the load is purely inductive: = 90°
• If the load is purely capacitive: = - 90°
• For a network that is primarily inductive, is positive (v leads i or i lags v)
• For a network that is primarily capacitive, is negative (i leads v)
Power in AC Circuit tVv m sin tIi m sin
4
• Positive power means that power has been distributed from supply into circuit.
• Negative power means that the power has been distributed from circuit into supply.
• There are three type of power in AC circuit:i) Average power, Pii) Apparent Power, S iii) Reactive Power, Q
Power in AC Circuit
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Average Power, P
• The average power (real power) is the power delivered to the load and dissipated by the load.
[watt, W]
Where, θ : phase angle between Vrms and Irms
OR ; [watt, W]
Power in AC Circuit
cosrmsrms IVP
RIP rms2
R
VP rms
2
6
14.5 Power Factor (Review)Average Power, P
• For a purely resistive load;
Hence;
• For purely inductive or purely capacitive load;
Hence;
0T
1cos PFrmsrmsIVP
90T0P
0cos PF
cosrmsrms IVP
7
Apparent Power, S
• From analysis of DC networks (and resistive elements above), it would seem apparent that the power delivered to the load is simply determined by P = VI, with no concern for the components of the load.
• However, in Chapter 14 (Lecture 10) the power factor (cos θ) of the load has a pronounced effect on the power dissipated, less pronounced for more reactive loads.
• Therefore P = VI is called apparent power, S.
[volt-amperes, VA]
Power in AC Circuit
rmsrmsIVS
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Apparent Power, S
OR ; [volt-amperes, VA]
• The average power to the load is;
However;
Therefore
• The power factor of a system Fp is
Power in AC Circuit
ZIS rms2
cosVIP
VIS
cosSP
S
PFp cos
Z
VS rms
2
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Reactive Power, Q
• In general, the reactive power associated with any circuit is defined to be
[volt-ampere reactive, VAR]
Where, θ : phase angle between Vrms and Irms
OR [volt-ampere reactive, VAR]
• For the resistor,
Power in AC Circuit
sinrmsrms IVQ
XIQ rms2
VAR 0Q
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Reactive Power, Q
• For a purely inductive circuit,
OR ;
Since the apparent power, S = VI , and the average power for inductor, P = 0
Power in AC Circuit
rmsrmsL IVQ
LrmsL XIQ 2
00
cos VIS
PFp
L
rmsL X
VQ
2
sinrmsrms IVQ
vL leads iL by 90°
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Reactive Power, Q
• For a purely capacitive circuit,
OR ;
Since the apparent power, S = VI , and the average power for capacitor, P = 0
Power in AC Circuit
rmsrmsC IVQ
CrmsC XIQ 2
00
cos VIS
PFp
C
rmsC X
VQ
2
sinrmsrms IVQ
iC leads vC by 90°
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19.7 Power Triangle
• The three quantities average power P, apparent power S and reactive power Q can be related in the vector domain by
with
90
90
0
CC
LL
Q
Q
P
Q
Q
P
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19.7 Power Triangle
• For an inductive load, the phasor power S, as it is often called, is defined by
S = P + jQL
• For a capacitive load, the phasor power S is defined by
S = P - jQC
22 QPS
14
• If a network has both capacitive and inductive elements, the reactive component of the power triangle will be determined by the difference between the reactive power delivered to each.
• If QL QC, the resultant power triangle will be similar to the inductive load power diagram.
• If QC QL, the resultant power triangle will be similar to the capacitive load power diagram.
• That the total reactive power is the difference between the reactive powers of the inductive and capacitive elements.
19.7 Power Triangle
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19.7 The Total P, Q, and SThe total number of watts PT, volt-amperes reactive QT, and volt-amperes ST, and the power factor Fp of any system can be found using the following procedure:
1. Find the real (average) power and reactive power for each branch of the circuit.
2. The total real power of the system (PT) is the sum of the average power delivered to each branch
3. The total reactive power (QT ) is the difference between the reactive power of the inductive loads and that of the capacitive loads.
4. The total apparent power is ST2 = PT
2 + QT2.
5. The total power factor is PT / ST. 22 QPS
16
There are two important points in the previous slide:
• First, the total apparent power, ST must be determined from the total average PT and total reactive powers QT and cannot be determined from the apparent powers of each branch.
• Second, and more important, it is not necessary to consider the series-parallel arrangement of branches. In other words, the total real PT , total reactive QT , or total apparent power ST is independent of whether the loads are in series, parallel, or series-parallel.
19.7 The Total P, Q, and S
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Example 19.3
1. Find the total number of watts PT, volt-amperes reactive QT, and volt-amperes ST and draw the power triangle.2. Find the power factor Fp
3. Find the current in phasor form.
19.7 The Total P, Q, and S
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Example 19.3 – Solution
1.
Load 1
VAR 0
W;100
1
1
Q
P
VA 100
01001
jS
22 QPS
19.7 The Total P, Q, and S
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Example 19.3 – solution (cont’d)
Load 2
VAR 700
W;200
2
2
Q
P
VA 728
7002002
jS
19.7 The Total P, Q, and S
22 QPS
20
Load 3
VAR 1500
W;300
3
3
Q
P
VA 71.1529
15003003
jS
Example 19.3 – solution (cont’d)
19.7 The Total P, Q, and S
22 QPS
21
Total
300200100321
PPPPT
Example 19.3 – solution (cont’d)
19.7 The Total P, Q, and S
W600TP
22
Total
VAR 800
15007000321
QQQQT
Example 19.3 – solution (cont’d)
19.7 The Total P, Q, and S
VAR(C) 800TQ
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Total
800600 j
jQPS TTT
The power triangle;
Example 19.3 – solution (cont’d)
19.7 The Total P, Q, and S
W600TP
VAR(C) 800TQ
VA 13.531000 TS
Note: ST is NOT equal to sum of each branch!!
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2. The power factor FP
VA 1000
W600
T
Tp S
PF
Example 19.3 – solution (cont’d)
19.7 The Total P, Q, and S
)( leading 6.0 CFp
25
3. The current
A 10V 100
VA 1000
VA 1000
VA 1000
I
I
VI
ST
Example 19.3 – solution (cont’d)
19.7 The Total P, Q, and S
)( leading 6.0 CFp
Since Fp is leading I leads E, predominantly capacitive circuit.
53.13 A 10I
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