Power and Energy
Measurements
Chapters: 39 and 42
Juha Kallunki, 5.4.2006
Contest

Power measurements
– DC circuits
– AC circuits



Three-phase systems
High-frequency power
measurements
Energy measurements
– DC circuits
– AC circuits

Example: Power and
energy measurements
in motor drives
Power in DC circuits




Power
P  I LVL
Can be carried out using a voltmeter and an
ammeter (generally)
Two measurement arrangements
Wattmeters:
–
–
–
–
Dynamometer
Digital wattmeter
Thermal wattmeter
Hall-power meter
DC circuits
a)
b)
Ammeter measures
current which flow
into the voltmeter
and load
Voltmeter
measures voltage
drop across the
ammeter in
addition to that
dropping across the
load
Dynamometer




Power (direct)
measurement device
for DC and AC systems
Accuracy better than
0,25 %
Two coils: static and
movable
Torque is proportional
product of current in
current coil and current
in voltage coil
Digital wattmeter (up to
100 kHz)

Advantages:
– High-resolution
– Accuracy


Several techniques
(multiplication of signals)
Electronic multiplier is an
analog system which gives
as its output a voltage
proportional to the power
indication required  A/D
conversion
Hall-power meter



Coil generates
magnetic field which is
proportional to load
current
The sensor excitation
current passes through
R1 and is proportional
to the load voltage
 Hall voltage is
proportional to load
power
Problems: offset and
linearity
Power in AC circuits




Instantaneous power
(time dependence)
Mean power (usually
the most interesting)
Real power (active
work), reactive power,
apparent power
Measures can be done
same way as DC circuit
(single-phase)
p(t )  v(t )i (t )
T
1
P   p(t )dt
T0
AC circuits
P  VL I L cos 
Q  VL I L sin 
S  P Q
2
2
Low- and MediumFrequency Power
Measurements

Three-Voltmeter
Method
– Single-phase
arrangements
– Power in load can
be measured using
a non-inductive
resistor and
measuring the three
voltage
– Also in DC circuits
2
2
2
VAC
 VAB
 VBC
PL 
2R
Line-Frequency Power
Measurements

Polyphase Power Measurements
– Three-phase systems are most commonly
used in industrial applications
– Energy and power generation and
distribution
– “Real power for consumer”
– Reactive power also important (loading)
– Power can measured several ways
– Power factor
Line-Frequency Power
Measurements (2)

Four (main) different cases which affects
to the measurement arrangements:
1.
2.
3.
4.
Symmetrical load with neutral conductor
Symmetrical load without neutral conductor
Unsymmetrical load with neutral conductor
Unsymmetrical load without neutral conductor
Line-Frequency Power
Measurements (3)

Measurements can be done several
ways (needed arrangements):
– One-wattmeter arrangements
– Two-wattmeter arrangements
– Three-wattmeter arrangements
Symmetrical and
Balanced systems


The supply system is symmetrical and the
three-phase load is balanced when phase
currents and voltages are equal
“Normal situation”
V1  V2  V3

 I1  I 2  I 3
Symmetrical load with
neutral conductor
Symmetrical load with
neutral conductor (2)




Number of wattmeters (voltage/current meter) is (n-1) where
n is number of conductors
If n=3, only one wattmeter are needed
Power factor can be measured for example with “power factor
meter”
Powers:
S  V1 I1  V2 I 2  V3 I 3

P  S cos 


Q  S sin 

Symmetrical load with
neutral conductor (3)

One wattmeter
arrangements for
real and reactive
power
measurements
P  3UT IT cos 
Symmetrical load without
neutral conductor



Active and reactive power
can be measured with two
power meter (in three-wire
system), case of
symmetrical load and
without neutral conductor
(motors), Aron’s theorem
Possible to use also in case
of unsymmetrical load
If power factor is <0,5 then
three wattmeter
arrangement
IA
PAB
A
VAB = VA - VB
Phase A
W
V
Phase B
VCB = VC - VB
IC
A
V
W
Phase C
PCB
P  PAB  PCD
Q  3 * PAB  PCD 
Symmetrical Power Systems
Supplying Unbalanced Loads



Current amplitudes are different, and
their relative phase is not equal 120°
Usually it is caused by some fault
(short circuit)
Three- or two wattmeter
arrangements (depends on neutral
point)
Symmetrical Power Systems
Supplying Unbalanced Loads

Four possible arrangements:
– Three-wattmeter arrangement
– Two-wattmeter arrangement
– Barbagelata arrangement
– Righi arrangement
Two-wattmeter
arrangements

Measurements
arrangements for
reactive power
measurements

Q  3  P1(30)  P3(10)

where

P1(30)  P10  P13
Barbagelata
arrangements


Measurement
arrangements for
active and reactive
power
measurements
“Two-wattmeter
method”
P  P12  P32


Q  1 2P  P   P  P 
13
31
32
12

3

Righi arrangements

Measurement
arrangements for
reactive power
measurements

1
Q
P32  P12  2 P2(31)
3

Conclusion about ThreeWire Systems
High-frequency power
measurements




Radio (< 300 MHz) or microwave (> 1
GHz) frequencies
Measurement devices are classified by
absorption type and transmitted or
throughline type
Based on thermistors, thermocouples,
diodes or radiation sensors
Should be calibrated very carefully
Thermistor-Based Power
Meters


A thermistor is
resistor made of a
compound of highly
temperature
metallic oxides
Resistance is a
function of the
temperature rise
produced by
applied power
Calorimetric method



Accurate method
Technique based on
direct determination
of the heat
produced by the
input power
“Laboratory
method”
Energy measurements

Simplest way is to measure current, voltage and observation
t1
interval and compute the product:
E  VIt   p(t )dt
t2


Observation interval measures by a chronometer or a time
counter
Electricity/energy meters:
– Electrodynamic measurement device
– Induction meter (AC)
– Digital energy meter (AC/DC)

Two main parts:
– Transducer (Converts power to mechanical or electrical signal)
– Counter (Integrates the “energy”)
DC Energy Measurements






Electrodynamic measurement
device (integrating wattmeter)
Based on DC motor (no iron)
Magnetic field is generating by
line current
Torque
kIV
C m
 k 2 IV 
R
Aluminum disk and permanent
magnet gives linear
dependence of Γ and power
Mechanical counter transfers
the rotating motion into a
digital or mechanical display
AC Energy Measurements



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

Induction energy meter
(every household)
Accuracy about 2 %
Current and voltage coil
AC current (coil)  Eddy
currents (disk)  Force
to disk
Variable powers cause
variable rotating speed
Day and night electricity
AC Energy measurements
1. Current coil and
magnetic circuit
2. Voltage coil and
magnetic circuit
3. Rotating disk
4. Disk axis
5. Permanent magnet
6. Display
Electronic Energy Meters



Product of current and voltage. The
result is integrated over the
observation time
The most used technique is the timedivision multiplier in which pulses are
modulated in duration and amplitude
of voltage and current
Accuracy: 0,005 %
Energy measurements

Automatic remote reading in future
– Pricing
– Controlling generation/loads


Several system under development
(GSM, radio link, phone line…)
Energy meters also in var (reactive
power) hours and volt-ampere
(apparent power) hours
Some Standards


General distribution network
SFS 2537
– AC energy measurements


Measurement arrangements
SFS 3381
– AC energy measurements

Measurement devices
Case: Elevators power and
energy consumption
measurements

”Two-wattmeter method”
–
–
–
–
–
Voltages: Ul1->Ul2 and Ul2 Ul3
Currents: I1 and I2
Sample frequency: 20 kHz
Dasylab™
P = 16 kW, n = 2780 rpm, I = 36 A / 47 A, I = 115 A (start),
cosphi = 0,86, height of the shaft = 3,9 m
Elevator power
consumption
80.00
67 .4 k
W m ax
L ni e ac tvi e pow e r
60.00
40.00
19 ,9 k
W *
20.00
0 .021 k
W
0 .170 k
W *
0.00
80.00
66 .8 k
W m ax
M o to r ac tvi e pow e r
60.00
40.00
19 .7 k
W *
20.00
0 .000 k
W *
0.00
2.5
L ni ePow e r

5.0
7.5
10.0
12.5
15.0
17.5
20.0
22.5
Moo
t rPow e r
Net (green) and motor (blue)
power
25.0
27.5
30.0
32.5
35.0
37.5
40.0
42.5
s
Elevator energy
consumption
80
71 .851W h
72 .602W h
72 .023W h
d t = 12 .102 s
70
60
A cce el ra toi n 21 .942W h (1 .176m )
D ece el ra toi n 0 .149W h (0 .472m )
50
F u llspeed 28 .463W h (2 .464m )
F u llspeed 0 .313W h (2 .664m )
40
30
D ece el ra toi n 20 .202W h (0 .344m )
A cce el ra toi n 0 .116W h (0 .816m )
20
10
0
2.5
Speed

5.0
7.5
10.0
12.5
Moo
t rA c ce el ra toi n
15.0
17.5
20.0
22.5
Ene rg y
Total (net) power
energy consumption
25.0
D si a
t n ce
27.5
30.0
32.5
35.0
37.5
40.0
42.5
s
The End