Classic Electrical Measurements 1

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1 DR. GYURCSEK ISTVÁN Classic Electrical Measurements 1 Indicating Measurement Instruments Sources and additional materials (recommended) S. Tumanski:Principles of electrical measurement, CRC Press ISBN Máté J.: Méréstechnika 1. PTE PMMIK, ERFP-DD2001-HU-B gyurcsek.istvan@mik.pte.hu

2 Introduction Moving Coil Meters Measuring Voltage and Current Moving Iron Meters Electrodynamic Meters Measuring Electrical Power Induction Type Watt-hour Meters 2 gyurcsek.istvan@mik.pte.hu

3 Indicating Instruments Eletromechanical devices Direct connection bw. moving part and measured signal No additional source (Power from investigated system) Affect on system (invasive method systematic error) Electronic analog devices Electronic circuits Additional power Hardly affect on measured system (non-invasive method) Electronic digital devices Digital circuits (also) Additional power Hardly affect on investigated system (non-invasive method) Compensators No affect on investigated system (non-invasive method) 3 gyurcsek.istvan@mik.pte.hu

4 Electromechanical vs. Digital Future, (today?) automatic (computer supported) measuring systems Electromechanical instruments still present (i.e. substitute such instruments in cars finished with not a success) Advantages Simplicity Reliability Low price No additional power Drawbacks No electrical output (need for operator s activity) Moving mechanical parts (sensitive to shocks) Parallax error Invasive measurement (power consumption) 4 gyurcsek.istvan@mik.pte.hu

5 Terms and Definitions Range [ X MAX, X MIN ] Lowest and highest measured value (given uncertainty) The interval in bw. range of measurement Sensitivity (differential) E = α X C = X MAX α MAX = R = X MAX X MIN = diff. of indication diff. of value Instrument Constant ( műszerállandó ) Measured value that causes unit (degree) indication Reciprocal of sensitivity limit of measurement scale end 5 gyurcsek.istvan@mik.pte.hu

6 Introduction Moving Coil Meters Measuring Voltage and Current Moving Iron Meters Electrodynamic Meters Measuring Electrical Power Induction Type Watt-hour Meters 6 gyurcsek.istvan@mik.pte.hu

7 Moving Coil Meters 1 Moving coil meters Deprez Instruments Simple (electrolitic) mean value Linear scale Symbol 7 gyurcsek.istvan@mik.pte.hu

Moving Coil Meters 2 M = Bndl I M torque B flux density n number of turns d diameter of coil l length of coil I current M S = k α k spring constant α angle of rotation M = M S α = Bndl

8 Moving Coil Meters 2 M = Bndl I M torque B flux density n number of turns d diameter of coil l length of coil I current M S = k α k spring constant α angle of rotation M = M S α = Bndl k E = α I = Bndl k I T 0 = 2π m k, T = T 0 P, b = 1 b2 2 mk T 0 period of oscillation T time constant b degree of damping P damping coefficient 8 gyurcsek.istvan@mik.pte.hu

9 Galvanometers (Deprez Instruments) Microammeter ( alapműszer ) Deprez device Spec. construction (extremely large sensitivity) Large sensitivity Bearingless moving elements Ribbon suspended coil (supplying wires and spring also) Low mass coil (frameless) Significant oscillation Large pointer or light indicator Principle of light indicator Ballastic galvanometer Large moment of inertia Measures charge instead of current Used as magnetic flux density. meter Fluxmeter Coil suspenden w/o. returning torque Integrating device Used as magnetic flux meter Both are replaced by electronic integrating devices 9 gyurcsek.istvan@mik.pte.hu

10 Introduction Moving Coil Meters Measuring Voltage and Current Moving Iron Meters Electrodynamic Meters Measuring Electrical Power Induction Type Watt-hour Meters

11 Voltage and Current Measurements Microammeter Voltmeter U x = I r + R d U x = U b r r + R d Default meter 60mV / 1mA (i.e.) U x = U b 1 + R d r R d r = U x U b 1 Default instrument params I - device current U b - device voltage r - internal resistance Supplementary params R d - series resistance R b - shunt resistance Ammeter mv meter R m r + R d I x = I x = I U b R m R b = U b R m + R b R m R b 1 + R m R b R m R b = I x I 1 11 gyurcsek.istvan@mik.pte.hu

12 Example 1 Four-wire Shunt MILLIVOLTMETER OR EVEN DVM 12 gyurcsek.istvan@mik.pte.hu

13 Example 2 - Input Attenuator of DVM Condition R LOAD = AC coupled AC compensated Asymmetric solution (Symmetric also possible) 13 gyurcsek.istvan@mik.pte.hu

14 Example 3 - Multi-Range VA meter Applied universal shunt same current I for various input currents (1) Preconditions I n I R n = I r + R d + R 1 R n millivoltmeter I n 1 I R n 1 = I r + R d + R 1 R n 1 (2) Result I n I 1 = R 1 R n U 5 14 gyurcsek.istvan@mik.pte.hu

calculated (depends on rectifier) Symbol U peak = 2 U MTR with PEAK rectifier U abs = U MTR 1.

15 Moving Coil Meters for AC Indicates DC values only (working principle) With the aid of rectifiers PEAK or ABS MEAN [ no RMS (*1) ] But scaled in RMS value (of pure sinusoidal signal) For non sinusoidals PEAK or ABS MEAN can be calculated (depends on rectifier) Symbol U peak = 2 U MTR with PEAK rectifier U abs = U MTR 1.11 with ABS MEAN rectifier (*1) more details: ABS, PEAK and true RMS Analogue Singal Processing later on 15 gyurcsek.istvan@mik.pte.hu

16 Introduction Moving Coil Meters Measuring Voltage and Current Moving Iron Meters Electrodynamic Meters Measuring Electrical Power Induction Type Watt-hour Meters

17 Moving Iron Meters 1 Symbol Measures RMS value (AC measurements!) Principle of operation Torque depends on I 2 M k = k α I 2 (current depts. on magnetic field & core flux ) Non-linear behavior k=k(α) [Máté Jenő: Méréstechnika ] L is angle dependent α = 1 2 k dl dα I2 BUT: construction dl dα I2 near linear! Stationary coil, moving iron ( attraction) Same magnetized moving and stationary iron ( push) 17 gyurcsek.istvan@mik.pte.hu

Moving Iron Meters 2 Construction of damping Main properties (summary) Advantages True RMS Simple, cheap Eeasy change of the range (selecting the number of the turns in the coil) Drawbacks Hysteresis

18 Moving Iron Meters 2 Construction of damping Main properties (summary) Advantages True RMS Simple, cheap Eeasy change of the range (selecting the number of the turns in the coil) Drawbacks Hysteresis of iron Hysteresis error (direction dependency) Exclusively for AC measurement Small sensitivity (to moving coil ) Large power consumption (abt VA) Low cut-off frequency (abt. 150 Hz) 18 gyurcsek.istvan@mik.pte.hu

19 Coffee break?

20 Introduction Moving Coil Meters Measuring Voltage and Current Moving Iron Meters Electrodynamic Meters Measuring Electrical Power Induction Type Watt-hour Meters

21 Electrodynamic Meters Electrodynamic meters wattmeters Symbol Formerly, most accurate indicating DEV Today, substituted by the digital DEV Still used as wattmeters. Principle of operation Two coils (stationary, moving) M = c I 1 I 2 cos φ Direct mesurement of power P = U I cos φ Linear scale for power Square scale for U or I 21 gyurcsek.istvan@mik.pte.hu

22 Introduction Moving Coil Meters Measuring Voltage and Current Moving Iron Meters Electrodynamic Meters Measuring Electrical Power Induction Type Watt-hour Meters

23 BACKUP: AC Power 1 Single-plase complex power S = U I = P + j Q Three-plase complex power S = U 1 I 1 + U 2 I 2 + U 3 I 3 S = P 1 + P 2 + P 3 + j Q 1 + Q 2 + Q 3 23 gyurcsek.istvan@mik.pte.hu

24 BACKUP: AC Power 2 S = U I = P + jq IND LOAD P > 0; Q > 0 φ = 0 90 Im IND SOURCE P < 0; Q > 0 φ = Re U φ φ I* CAP LOAD P > 0; Q < 0 φ = 0 90 CAP SOURCE P < 0; Q < 0 φ = gyurcsek.istvan@mik.pte.hu

25 BACKUP: AC Power 3 S = U I = P + jq CAP LOAD P > 0; Q > 0 φ = 0 90 Im CAP SOURCE P < 0; Q > 0 φ = Re U* φ φ I IND LOAD P > 0; Q < 0 φ = 0 90 IND SOURCE P < 0; Q < 0 φ = gyurcsek.istvan@mik.pte.hu

26 Measuring Electric Power Measuring principle M = c I 1 I 2 cos φ P = U I cos φ M = c 1 U I cos φ = k P R d 26 gyurcsek.istvan@mik.pte.hu

27 Three-Phase Power Measurement P = P W1 + P W2 + P W3 Three separate meters OR One meter with three electrodynamic devices (common axle) In case of balanced load one meter (enough) P = 3 P W1 Measurement w. neutral wire Measurement w/o. neutral wire 27 gyurcsek.istvan@mik.pte.hu

28 Three-Phase Reactive Power In case of balanced voltage system W3 P W1 = I 1 U 23 cos 90 φ = 3U 1 I 1 sin φ = 3Q 1 Symmetric voltage system (unbalanced load OK) Q = P W1 + P W2 + P W gyurcsek.istvan@mik.pte.hu

29 Aron Method 1 Aron Method - for Three-wire System! Three-phase system w/o. neutral wire (three-wire system) Two wattmeters enough Instantaneous power p = u 1 i 1 + u 2 i 2 + u 3 i 3 Three-wire system (only condition!) i 1 + i 2 + i 3 = 0 i 3 = i 1 + i 2 substituting p = u 1 u 3 i 1 + u 2 u 3 i 2 p = u 13 i 1 + u 23 i 2 T P = 1 T න 0 p dt = U 13 I 1 cos U 13, I 1 + U 23 I 2 cos U 23, I 2 = P W1 + P W2 29 gyurcsek.istvan@mik.pte.hu

30 Aron Method 2 in case of balanced load P W1 = U L I P cos 30 φ P W2 = U L I P cos 30 + φ easy to prove (HW!) φ = tan 1 3 P W1 P W2 P W1 + P W2 Advantage of Aron method Economical (often used) cheap wattmeters BUT expensive measuring transformers (isolate & reduce U, I) Drawbacks of Aron method Three-wire system required! Incorrect result in case of Short circuiting to ground Leakage current ( szivárgási áram ) Q = 3 P W1 P W2 30 gyurcsek.istvan@mik.pte.hu

31 Aron Method 3 P I and P II depending on φ P I = U RS I R cos U RS, I R P II = U ST I T cos U ST, I T a) cos φ=0.5 CAP Load P II =0 b) cos φ=0.5 IND Load, P I =0 c) cos φ=1 P I =P II If cos φ<0,5 P I < 0 or P II < 0! R R R T S T S T S 31 gyurcsek.istvan@mik.pte.hu

32 Introduction Moving Coil Meters Measuring Voltage and Current Moving Iron Meters Electrodynamic Meters Measuring Electrical Power Induction Type Watt-hour Meters

33 Induction Type Watt-Hour Meters 1 Induction watt-hour meters energy meters Still present Drawbacks No output signal (manual readings) Complex system of error correction Slow replacement proc. (millions of devices). Principle of operation (Ferrari s system) In two independent cores U Φ U, I Φ I Eddy currents in rotating ALU disc Rotating torque M r (interact of fluxes and eddy currents) M r = c ω I 1 I 2 sin I 1, I 2 33 gyurcsek.istvan@mik.pte.hu

34 Induction Type Watt-Hour Meters 2 M r = c ω I 1 I 2 sin I 1, I 2 I 1 = I, I 2 = U ω L U L U L I φ UI 90 sin I 1, I 2 cos U, I U M r c ω I cos φ = c P = c P ω L U L u Breaking magnet vs. its eddy currents M B (braking torque) M B = k B ω M r + M B = c P k B ω = 0 ω = c k B P = k P n = k n P (n proport. to P, like asynchronous motors) Mech. register counts N energy consumed by the load. N = n t = k n P t = k n W 34 gyurcsek.istvan@mik.pte.hu

φ UI 90 ) Additional magnetic shunt (bcs.

35 Induction Type Watt-Hour Meters 3 Corrections (goal error characteristics below the limits) Additional phase correction winding (bcs. φ UI 90 ) Additional magnetic shunt (bcs. 2 cores have also M B ) Friction compensation of ALU disc bearings Weakness: corrections changes with the aging process 35 gyurcsek.istvan@mik.pte.hu

36 Three-Phase Active Consumption Measuring Active Consumption in Three-phase System (Aron Method) Direct measurement Using Voltage and Current Transformers

37 Three-Phase Reactive Consumption Measuring Reactive Consumption in Three-Phase System (Aron Method) Direct measurement Using Voltage and Current Transformers

38 Questions

Work, Energy and Power

1 Work, Energy and Power Work is an activity of force and movement in the direction of force (Joules) Energy is the capacity for doing work (Joules) Power is the rate of using energy (Watt) P = W / t,