Fundamentals Mechanical Power of Power2 Wattmeter Method 3 Wattmeter Method ƒ Time Domain equency...
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Fundamentals of Power Measurement Unit Relationships Average, RMS, Peak, Peak-to-Peak Conversation Known Value Average RMS Peak Peak-to-Peak Average 1.0 1.11 1.57 3.14 RMS 0.9 1.0 1.414 2.828 Peak 0.637 0.707 1.0 2.0 Peak-to-Peak 0.32 0.3535 0.5 1.0 Three Phase System Balanced three phase diagram V line-line = V line-neutral 3 � ❉ Mechanical Power P m = x Torque 2 x π x Rotating Speed 60 (Sec/Min) Synchronous Speed = 120 x Frequency Number of Poles Electrical Power DC Power Measurement Watts W = V x A AC Power Measurement Active Power Watts P = V rms x A rms x Cosɸ Reactive Power VARS Q = V rms x A rms x Sin ɸ Apparent Power Volt-Amps S = V rms x A rms Efficiency = Output Power Input Power = P m Electrical Input Power ɸ P Q S POWER RELATIONSHIPS VOLT-AMPS VARS WATTS Displacement Power Factor PF = Cosɸ True Power Factor The Precision Makers A WORD OF CAUTION NEVER Open circuit the secondary side of a current transformer while it is energized! This could cause serious damage to the CT and could possibly be harmful to equipment operators. W VA PF = WATTS P = Power VOLTS V = Voltage AMPS I = Current OHMS R = Resistance � � PxR V x I I x R I 2 x R V 2 — R P — I P — I 2 V 2 — P V — R P — V V — I P — R Watts P Amps I V Volts R Ohms
Transcript of Fundamentals Mechanical Power of Power2 Wattmeter Method 3 Wattmeter Method ƒ Time Domain equency...
Fundamentalsof Power
Measurement
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Unit Relationships
Average, RMS, Peak,Peak-to-Peak Conversation
Known Value Average RMS Peak Peak-to-Peak
Average 1.0 1.11 1.57 3.14
RMS 0.9 1.0 1.414 2.828
Peak 0.637 0.707 1.0 2.0
Peak-to-Peak 0.32 0.3535 0.5 1.0
Three Phase System
Balanced three phase diagram
V line-line = V line-neutral3� ❉
Mechanical Power
Pm = x Torque2 x π x Rotating Speed
60 (Sec/Min)
Synchronous Speed = 120 x FrequencyNumber of Poles
Electrical PowerDC Power Measurement
Watts W = V x A
AC Power Measurement
Active Power
Watts P = Vrms x Arms x Cosɸ
Reactive Power
VARS Q = Vrms x Arms x Sinɸ
Apparent Power
Volt-Amps S = Vrms x Arms
Efficiency = Output PowerInput Power = Pm
ElectricalInput Power
ɸP
QSPOWER RELATIONSHIPS
VOLT-AMPS VARS
WATTS
Blondel TransformationBlondel theory states that total power is measured with
ONE LESS wattmeter than the number of WIRES.
1-P 2-W 1 Wattmeter1-P 3-W 2 Wattmeters3-P 3-W 2 Wattmeters3-P 3-W 3 Wattmeters3-P 4-W 3 Wattmeters
Displacement Power Factor
PF = Cosɸ
True Power Factor
Harmonic Measurements
∑
Ʃ
Ʃ
Ʃ
���
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P = ∫0
T v(t) * i (t) dt
∫0
T v(t)2 dt
∫0
T i(t)2 dt
URMS =
IRMS = I =
U =
P = P (k)
U (k )2
I (k ) 2
max
max
max
k = min
k = min
k = min
k = Harmonic Order; 1, 2, 3, . . .etc
k = Harmonic Order; 1, 2, 3, . . .etc
Harmonics ModeNOT True RMS Measurement
Typical UL and CSA Method
Typical IEC Method
* 100
* 100
ITHD =
ITHD =
max
k = 2
I (k=1)
I (k)2
Normal ModeTrue RMS Measurement
ThePrecisionMakers
Functions WT1800Power Analyzer
DLM2000Oscilloscope
Bandwidth DC - 2MHz DC - 500MHzPower DC - 50MHz
Accuracy 0.05% reading +0.1% range
Calibrated Traceable Measurement System
1.5% at input terminals, at DC
Power approx at 3.5%Based on Probe Accuracy
Input Method Direct Connections to High Voltage & High Current
Probes for high frequency & small currents
Resolution Typical 16-bit 65,636 levels
Typical 8-bit256 levels
PFT =Wa + Wb
(VAa + VAb)
�PFT =
Wa + Wb
33 (VAa + VAb + VAc)
∑���max
k = 2
I ( Total )
I (k)2
ACSource
A
V
V
W
W
+-
+-
+-
V(t)
V(t)
I(t)
One-phaseThree-wire
Load1P-3W
I(t)
A
Phase A
Phase B
Neutral
a
b
ACSource
AW
+-
V
V
Three-phaseThree-wire
Load3P-3W
Phase A
Phase C
Phase B
a
ab
cb
W+-
bA
W+-c
A +-
Vac
+-+-
V
V
V
ACSource
AW
+-
V
V
Three-phaseThree-wire
Load3V-3A
Phase A
Phase C
Phase B
a
ab
cb
W+-
bA
W+-c
A +-
Vac
+-+-
V
V
V
Three-phaseFour-wire
Load3P-4W
Van
Vbn
Vcn
AW
+-c
AW
+-b
AW
+-a
V
V
V
Phase A
Phase C
Phase BAC
Source
+-
ACSource
A
VW
+-
+-
V(t)I(t) One-phase
Two-wireLoad
1P-2W
a
PT = Wa + Wb
PT = Wa + Wb
PT = Wa + Wb
PT = Wa + Wb + Wc
A WORD OF CAUTION
NEVER Open circuit the secondary side of a current transformer while it is energized!
This could cause serious damage to the CT and could possibly be harmful to equipment operators.
Power Analyzer vs Oscilloscope
�PFT =
Wa + Wb
32 (VAa + VAb)
PFT =Wa + Wb + Wc
(VAa + VAb + VAc)
PT = Wa
PFT =Wa
VAa
1 Wattmeter Method
2 Wattmeter Method
3 Wattmeter Method
ƒ
Frequency DomainTime Domain
time
Ampl
itude
Elements of a distortedor non-sinusoidalwaveform consist of Sine Waves of various:� Amplitudes� Frequencies� Phase
Because of the Phasedifference in some ofthe harmonics, negative,or reverse power canactually be produced.
Harmonics are defined as Voltages, Currents or Power at frequencies that are a multiple of the fundamental frequency.Total Power of the Distorted Waveform is calculated as:Ptotal= V0 x I0 + V1 x I1 x Cosθ1 + V2 x I2 x Cosθ2 + V3 x I3 x Cos03 +...+Vn x In x Cosθn
OR More Precisely
Ptotal= V0 x I0 + Ʃmin Vn x In x Cosθn
Distorted AC Waveforms
1T
1T
1T
WVAPF =
Yokogawa Deutschland GmbH | Tel. +49 8152 9310-0 | [email protected] | tmi.yokogawa.com/de
Test&Measurement
WATTSP = Power
VOLTSV = Voltage
AMPSI = Current
OHMSR = Resistance
�
�PxR
V x I
I x R
I2 x R
V2
—R
P—IP— I2
V2
—P
V— R P—V
V—I
P— RWatts
PAmps
IV
VoltsR
Ohms
Fundamentalsof Power
Measurement
����
����
Unit Relationships
Average, RMS, Peak,Peak-to-Peak Conversation
Known Value Average RMS Peak Peak-to-Peak
Average 1.0 1.11 1.57 3.14
RMS 0.9 1.0 1.414 2.828
Peak 0.637 0.707 1.0 2.0
Peak-to-Peak 0.32 0.3535 0.5 1.0
Three Phase System
Balanced three phase diagram
V line-line = V line-neutral3� ❉
Mechanical Power
Pm = x Torque2 x π x Rotating Speed
60 (Sec/Min)
Synchronous Speed = 120 x FrequencyNumber of Poles
Electrical PowerDC Power Measurement
Watts W = V x A
AC Power Measurement
Active Power
Watts P = Vrms x Arms x Cosɸ
Reactive Power
VARS Q = Vrms x Arms x Sinɸ
Apparent Power
Volt-Amps S = Vrms x Arms
Efficiency = Output PowerInput Power = Pm
ElectricalInput Power
ɸP
QSPOWER RELATIONSHIPS
VOLT-AMPS VARS
WATTS
Blondel TransformationBlondel theory states that total power is measured with
ONE LESS wattmeter than the number of WIRES.
1-P 2-W 1 Wattmeter1-P 3-W 2 Wattmeters3-P 3-W 2 Wattmeters3-P 3-W 3 Wattmeters3-P 4-W 3 Wattmeters
Displacement Power Factor
PF = Cosɸ
True Power Factor
Harmonic Measurements
∑
Ʃ
Ʃ
Ʃ
���
����
����
P = ∫0
T v(t) * i (t) dt
∫0
T v(t)2 dt
∫0
T i(t)2 dt
URMS =
IRMS = I =
U =
P = P (k)
U (k )2
I (k ) 2
max
max
max
k = min
k = min
k = min
k = Harmonic Order; 1, 2, 3, . . .etc
k = Harmonic Order; 1, 2, 3, . . .etc
Harmonics ModeNOT True RMS Measurement
Typical UL and CSA Method
Typical IEC Method
* 100
* 100
ITHD =
ITHD =
max
k = 2
I (k=1)
I (k)2
Normal ModeTrue RMS Measurement
ThePrecisionMakers
Functions WT1800Power Analyzer
DLM2000Oscilloscope
Bandwidth DC - 2MHz DC - 500MHzPower DC - 50MHz
Accuracy 0.05% reading +0.1% range
Calibrated Traceable Measurement System
1.5% at input terminals, at DC
Power approx at 3.5%Based on Probe Accuracy
Input Method Direct Connections to High Voltage & High Current
Probes for high frequency & small currents
Resolution Typical 16-bit 65,636 levels
Typical 8-bit256 levels
PFT =Wa + Wb
(VAa + VAb)
�PFT =
Wa + Wb
33 (VAa + VAb + VAc)
∑���max
k = 2
I ( Total )
I (k)2
ACSource
A
V
V
W
W
+-
+-
+-
V(t)
V(t)
I(t)
One-phaseThree-wire
Load1P-3W
I(t)
A
Phase A
Phase B
Neutral
a
b
ACSource
AW
+-
V
V
Three-phaseThree-wire
Load3P-3W
Phase A
Phase C
Phase B
a
ab
cb
W+-
bA
W+-c
A +-
Vac
+-+-
V
V
V
ACSource
AW
+-
V
V
Three-phaseThree-wire
Load3V-3A
Phase A
Phase C
Phase B
a
ab
cb
W+-
bA
W+-c
A +-
Vac
+-+-
V
V
V
Three-phaseFour-wire
Load3P-4W
Van
Vbn
Vcn
AW
+-c
AW
+-b
AW
+-a
V
V
V
Phase A
Phase C
Phase BAC
Source
+-
ACSource
A
VW
+-
+-
V(t)I(t) One-phase
Two-wireLoad
1P-2W
a
PT = Wa + Wb
PT = Wa + Wb
PT = Wa + Wb
PT = Wa + Wb + Wc
A WORD OF CAUTION
NEVER Open circuit the secondary side of a current transformer while it is energized!
This could cause serious damage to the CT and could possibly be harmful to equipment operators.
Power Analyzer vs Oscilloscope
�PFT =
Wa + Wb
32 (VAa + VAb)
PFT =Wa + Wb + Wc
(VAa + VAb + VAc)
PT = Wa
PFT =Wa
VAa
1 Wattmeter Method
2 Wattmeter Method
3 Wattmeter Method
ƒ
Frequency DomainTime Domain
time
Ampl
itude
Elements of a distortedor non-sinusoidalwaveform consist of Sine Waves of various:� Amplitudes� Frequencies� Phase
Because of the Phasedifference in some ofthe harmonics, negative,or reverse power canactually be produced.
Harmonics are defined as Voltages, Currents or Power at frequencies that are a multiple of the fundamental frequency.Total Power of the Distorted Waveform is calculated as:Ptotal= V0 x I0 + V1 x I1 x Cosθ1 + V2 x I2 x Cosθ2 + V3 x I3 x Cos03 +...+Vn x In x Cosθn
OR More Precisely
Ptotal= V0 x I0 + Ʃmin Vn x In x Cosθn
Distorted AC Waveforms
1T
1T
1T
WVAPF =
Yokogawa Deutschland GmbH | Tel. +49 8152 9310-0 | [email protected] | tmi.yokogawa.com/de
Test&Measurement
WATTSP = Power
VOLTSV = Voltage
AMPSI = Current
OHMSR = Resistance
�
�PxR
V x I
I x R
I2 x R
V2
—R
P—IP— I2
V2
—P
V— R P—V
V—I
P— RWatts
PAmps
IV
VoltsR
Ohms
