Power and Energy Power and Energy MeasurementsMeasurementsChapters: 39 and 42Chapters: 39 and 42

Juha Kallunki, 5.4.2006Juha Kallunki, 5.4.2006

ContestContest Power measurementsPower measurements

– DC circuitsDC circuits– AC circuitsAC circuits

Three-phase systemsThree-phase systems High-frequency power High-frequency power

measurementsmeasurements Energy measurementsEnergy measurements

– DC circuitsDC circuits– AC circuitsAC circuits

Example: Power and Example: Power and energy measurements energy measurements in motor drivesin motor drives

Power in DC circuitsPower in DC circuits Power Power Can be carried out using a voltmeter Can be carried out using a voltmeter

and an ammeter (generally)and an ammeter (generally) Two measurement arrangementsTwo measurement arrangements Wattmeters:Wattmeters:

– DynamometerDynamometer– Digital wattmeterDigital wattmeter– Thermal wattmeterThermal wattmeter– Hall-power meterHall-power meter

LLVIP

DC circuitsDC circuits

a)a) Ammeter measures Ammeter measures current which flow current which flow into the voltmeter into the voltmeter and load and load

b)b) Voltmeter Voltmeter measures voltage measures voltage drop across the drop across the ammeter in ammeter in addition to that addition to that dropping across the dropping across the load load

DynamometerDynamometer Power (direct) Power (direct)

measurement device measurement device for DC and AC for DC and AC systemssystems

Accuracy better than Accuracy better than 0,25 %0,25 %

Two coils: static and Two coils: static and movablemovable

Torque is proportional Torque is proportional product of current in product of current in current coil and current coil and current in voltage coilcurrent in voltage coil

Digital wattmeter (up Digital wattmeter (up to 100 kHz)to 100 kHz) Advantages:Advantages:

– High-resolutionHigh-resolution– AccuracyAccuracy

Several techniques Several techniques (multiplication of (multiplication of signals)signals)

Electronic multiplier is Electronic multiplier is an analog system which an analog system which gives as its output a gives as its output a voltage proportional to voltage proportional to the power indication the power indication required required A/D A/D conversionconversion

Hall-power meterHall-power meter Coil generates Coil generates

magnetic field which magnetic field which is proportional to load is proportional to load currentcurrent

The sensor excitation The sensor excitation current passes current passes through R1 and is through R1 and is proportional to the proportional to the load voltageload voltage Hall voltage is Hall voltage is proportional to load proportional to load powerpower

Problems: offset and Problems: offset and linearitylinearity

Power in AC circuitsPower in AC circuits Instantaneous power Instantaneous power

(time dependence)(time dependence) Mean power (usually Mean power (usually

the most interesting)the most interesting) Real power (active Real power (active

work), reactive power, work), reactive power, apparent powerapparent power

Measures can be done Measures can be done same way as DC same way as DC circuit (single-phase)circuit (single-phase)

)()()( titvtp

T

dttpT

P0

)(1

AC circuitsAC circuits

cosLLIVP sinLLIVQ 22 QPS

Low- and Medium-Low- and Medium-Frequency Power Frequency Power MeasurementsMeasurements Three-Voltmeter Three-Voltmeter

MethodMethod– Single-phase Single-phase

arrangementsarrangements– Power in load can Power in load can

be measured be measured using a non-using a non-inductive resistor inductive resistor and measuring and measuring the three voltagethe three voltage

– Also in DC circuitsAlso in DC circuits

RVVVP BCABAC

L 2

222

Line-Frequency Power Line-Frequency Power MeasurementsMeasurements Polyphase Power MeasurementsPolyphase Power Measurements

– Three-phase systems areThree-phase systems are most commonly most commonly usedused in in industrial applicationsindustrial applications

– Energy and power generation and Energy and power generation and distributiondistribution

– ““Real power for consumer”Real power for consumer”– Reactive power also important (loading) Reactive power also important (loading) – Power can measured several waysPower can measured several ways– Power factorPower factor

Line-Frequency Power Line-Frequency Power Measurements (2)Measurements (2) Four (main) different cases which Four (main) different cases which

affects to the measurement affects to the measurement arrangements:arrangements:

1.1. Symmetrical load with neutral conductorSymmetrical load with neutral conductor2.2. Symmetrical load without neutral Symmetrical load without neutral

conductorconductor3.3. Unsymmetrical load with neutral Unsymmetrical load with neutral

conductorconductor4.4. Unsymmetrical load without neutral Unsymmetrical load without neutral

conductorconductor

Line-Frequency Power Line-Frequency Power Measurements (3)Measurements (3) Measurements can be done Measurements can be done

several ways (needed several ways (needed arrangements):arrangements):– One-wattmeter arrangementsOne-wattmeter arrangements– Two-wattmeter arrangementsTwo-wattmeter arrangements– Three-wattmeter arrangementsThree-wattmeter arrangements

Symmetrical and Symmetrical and Balanced systemsBalanced systems

The supply system is symmetrical and the The supply system is symmetrical and the three-phase load is balanced when phase three-phase load is balanced when phase currents and voltages are equalcurrents and voltages are equal

““Normal situation”Normal situation”

321

321

IIIVVV

Symmetrical load with Symmetrical load with neutral conductorneutral conductor

Symmetrical load with Symmetrical load with neutral conductor (2)neutral conductor (2) Number of wattmeters (voltage/current meter) is (Number of wattmeters (voltage/current meter) is (nn-1) -1)

where where nn is number of conductors is number of conductors If If n=3, n=3, only one wattmeter are neededonly one wattmeter are needed Power factor can be measured for example with Power factor can be measured for example with

“power factor meter” “power factor meter” Powers:Powers:

sincos

332211

SQSP

IVIVIVS

Symmetrical load with Symmetrical load with neutral conductor (3)neutral conductor (3) One wattmeter One wattmeter

arrangements for arrangements for real and reactive real and reactive power power measurementsmeasurements

cos3 TT IUP

Symmetrical load Symmetrical load without neutral without neutral conductorconductor Active and reactive Active and reactive

power can be measured power can be measured with two power meter with two power meter (in three-wire system), (in three-wire system), case of symmetrical case of symmetrical load and without neutral load and without neutral conductor (motors), conductor (motors), Aron’s theoremAron’s theorem

Possible to use also in Possible to use also in case of unsymmetrical case of unsymmetrical loadload

If power factor is <0,5 If power factor is <0,5 then three wattmeter then three wattmeter arrangementarrangement

CDAB PPP

CDAB PPQ *3

A

A

V

V

W

W

Phase A

Phase B

Phase C

VAB = VA - VB

VCB = VC - VB

IA

IC

PAB

PCB

Symmetrical Power Symmetrical Power Systems Supplying Systems Supplying Unbalanced LoadsUnbalanced Loads Current amplitudes are different, Current amplitudes are different,

and their relative phase is not and their relative phase is not equal 120°equal 120°

Usually it is caused by some fault Usually it is caused by some fault (short circuit)(short circuit)

Three- or two wattmeter Three- or two wattmeter arrangements (depends on neutral arrangements (depends on neutral point)point)

Symmetrical Power Symmetrical Power Systems Supplying Systems Supplying Unbalanced LoadsUnbalanced Loads Four possible arrangements:Four possible arrangements:

– Three-wattmeter arrangementThree-wattmeter arrangement– Two-wattmeter arrangementTwo-wattmeter arrangement– Barbagelata arrangementBarbagelata arrangement– Righi arrangementRighi arrangement

Two-wattmeter Two-wattmeter arrangementsarrangements Measurements Measurements

arrangements for arrangements for reactive power reactive power measurementsmeasurements

wherewhere

)10(3)30(13 PPQ

1310)30(1 PPP

Barbagelata Barbagelata arrangementsarrangements Measurement Measurement

arrangements for arrangements for active and active and reactive power reactive power measurementsmeasurements

““Two-wattmeter Two-wattmeter method”method”

12323113

3212

23

1 PPPPQ

PPP

Righi arrangementsRighi arrangements Measurement Measurement

arrangements for arrangements for reactive power reactive power measurementsmeasurements

)31(21232 23

1 PPPQ

Conclusion about Conclusion about Three-Wire SystemsThree-Wire Systems

High-frequency power High-frequency power measurementsmeasurements Radio (< 300 MHz) or microwave (> Radio (< 300 MHz) or microwave (>

1 GHz) frequencies1 GHz) frequencies Measurement devices are classified Measurement devices are classified

by absorption type and transmitted by absorption type and transmitted or throughline typeor throughline type

Based on thermistors, Based on thermistors, thermocouples, diodes or radiation thermocouples, diodes or radiation sensorssensors

Should be calibrated very carefullyShould be calibrated very carefully

Thermistor-Based Thermistor-Based Power MetersPower Meters A thermistor is A thermistor is

resistor made of a resistor made of a compound of compound of highly temperature highly temperature metallic oxidesmetallic oxides

Resistance is a Resistance is a function of the function of the temperature rise temperature rise produced by produced by applied powerapplied power

Calorimetric methodCalorimetric method Accurate methodAccurate method Technique based Technique based

on direct on direct determination of determination of the heat the heat produced by the produced by the input power input power

““Laboratory Laboratory method”method”

EnergyEnergy measurementsmeasurements Simplest way is to measure current, voltage and Simplest way is to measure current, voltage and

observation interval and compute the product:observation interval and compute the product:

Observation interval measures by a chronometer or a Observation interval measures by a chronometer or a time countertime counter

Electricity/energy meters:Electricity/energy meters:– Electrodynamic measurement deviceElectrodynamic measurement device– Induction meter (AC)Induction meter (AC)– Digital energy meter (AC/DC)Digital energy meter (AC/DC)

Two main parts:Two main parts:– Transducer (Converts power to mechanical or electrical Transducer (Converts power to mechanical or electrical

signal)signal)– Counter (Integrates the “energy”)Counter (Integrates the “energy”)

1

2

)(t

t

dttptVIE

DC Energy DC Energy MeasurementsMeasurements Electrodynamic Electrodynamic

measurement device measurement device (integrating wattmeter)(integrating wattmeter)

Based on DC motor (no iron)Based on DC motor (no iron) Magnetic field is generating Magnetic field is generating

by line currentby line current Torque Torque

Aluminum disk and Aluminum disk and permanent magnet gives permanent magnet gives linear dependence of linear dependence of ΓΓ and and power power

Mechanical counter transfers Mechanical counter transfers the rotating motion into a the rotating motion into a digital or mechanical displaydigital or mechanical display

Vm IkRkIVC 2

AC AC EnergyEnergy MeasurementsMeasurements Induction energy Induction energy

meter (every meter (every household)household)

Accuracy about 2 %Accuracy about 2 % Current and voltage Current and voltage

coilcoil AC current (coil) AC current (coil)

Eddy currents (disk) Eddy currents (disk) Force to diskForce to disk

Variable powers cause Variable powers cause variable rotating speedvariable rotating speed

Day and night Day and night electricityelectricity

AC Energy AC Energy measurementsmeasurements

1.1. Current coil and Current coil and magnetic circuitmagnetic circuit

2.2. Voltage coil and Voltage coil and magnetic circuitmagnetic circuit

3.3. Rotating diskRotating disk4.4. Disk axisDisk axis5.5. Permanent Permanent

magnetmagnet6.6. DisplayDisplay

Electronic Energy Electronic Energy MetersMeters Product of current and voltage. The Product of current and voltage. The

result is integrated over the result is integrated over the observation timeobservation time

The most used technique is the The most used technique is the time-division multiplier in which time-division multiplier in which pulses are modulated in duration pulses are modulated in duration and amplitude of voltage and and amplitude of voltage and currentcurrent

Accuracy: 0,005 %Accuracy: 0,005 %

Energy measurementsEnergy measurements Automatic remote reading in future Automatic remote reading in future

– PricingPricing– Controlling generation/loadsControlling generation/loads

Several system under development Several system under development (GSM, radio link, phone line…)(GSM, radio link, phone line…)

Energy meters also in var (reactive Energy meters also in var (reactive power) hours and volt-ampere power) hours and volt-ampere (apparent power) hours(apparent power) hours

Some StandardsSome Standards General distribution networkGeneral distribution network SFS 2537SFS 2537

– AC energy measurementsAC energy measurements Measurement arrangementsMeasurement arrangements

SFS 3381SFS 3381– AC energy measurementsAC energy measurements

Measurement devicesMeasurement devices

Case: Elevators power Case: Elevators power and energy consumption and energy consumption measurementsmeasurements ””Two-wattmeter method”Two-wattmeter method”

– Voltages: UVoltages: Ul1l1->U->Ul2l2 and U and Ul2l2 U Ul3l3– Currents: ICurrents: I11 and I and I22– Sample frequency: 20 kHz Sample frequency: 20 kHz – Dasylab™Dasylab™– P = 16 kW, n = 2780 rpm, I = 36 A / 47 A, I = 115 A 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(start), cosphi = 0,86, height of the shaft = 3,9 m

Elevator power Elevator power consumptionconsumption

s

2 . 5 5 . 0 7 . 5 1 0 . 0 1 2 . 5 1 5 . 0 1 7 . 5 2 0 . 0 2 2 . 5 2 5 . 0 2 7 . 5 3 0 . 0 3 2 . 5 3 5 . 0 3 7 . 5 4 0 . 0 4 2 . 5L i n e P o w e r M o to r P o w e r

8 0 . 0 0

6 0 . 0 0

4 0 . 0 0

2 0 . 0 0

0 . 0 08 0 . 0 0

6 0 . 0 0

4 0 . 0 0

2 0 . 0 0

0 . 0 0

1 9 , 9 k W *

L i n e a c t i v e p o w e r

M o t o r a c t i v e p o w e r

1 9 . 7 k W *

0 . 1 7 0 k W *

0 . 0 0 0 k W *

0 . 0 2 1 k W

6 7 . 4 k W m a x

6 6 . 8 k W m a x

Net (green) and motor Net (green) and motor (blue) power(blue) power

Elevator energy Elevator energy consumptionconsumption

s2 . 5 5 . 0 7 . 5 1 0 . 0 1 2 . 5 1 5 . 0 1 7 . 5 2 0 . 0 2 2 . 5 2 5 . 0 2 7 . 5 3 0 . 0 3 2 . 5 3 5 . 0 3 7 . 5 4 0 . 0 4 2 . 5

S p e e d M o to r A c c e l e r a t i o n E n e r g y D i s t a n c e

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

0

A c c e le r a t i o n 2 1 . 9 4 2 W h ( 1 . 1 7 6 m )

F u l l s p e e d 2 8 . 4 6 3 W h ( 2 . 4 6 4 m )

D e c e le r a t i o n 2 0 . 2 0 2 W h ( 0 . 3 4 4 m )

7 1 . 8 5 1 W h 7 2 . 0 2 3 W h

A c c e le r a t i o n 0 . 1 1 6 W h ( 0 . 8 1 6 m )

F u l l s p e e d 0 . 3 1 3 W h ( 2 . 6 6 4 m )

D e c e l e r a t i o n 0 . 1 4 9 W h ( 0 . 4 7 2 m )

7 2 . 6 0 2 W hd t = 1 2 . 1 0 2 s

Total (net) power Total (net) power energyenergy consumptionconsumption

The The EndEnd