Electrical Measurements and Instruments (EX-303) - Unit 1 Short Notes

UNIT 1: ELECTRICAL MEASUREMENTS AND INSTRUMENTS

1.0 FUNDAMENTALS OF MEASUREMENT & ERROR ANALYSIS

1.1 Types of Errors in Measurement

• Gross Errors: Human mistakes (reading, recording). Preventable by care and averaging.

• Systematic Errors: Consistent, predictable. Sub-classified as:

  • Instrumental: Due to instrument limitations (e.g., calibration error, wear).

  • Environmental: Due to external conditions (temperature, humidity, magnetic field).

  • Observational: Due to observer's habit or parallax.

  • Can be minimized by calibration, correction factors, or improved technique.

• Random Errors: Unpredictable variations (e.g., noise). Reduced by repeated measurements and statistical analysis.

[!TIP] EXAM TIP: Be prepared to classify a given error and suggest its minimization. Gross errors are not part of instrument specifications.

1.2 Static Characteristics of Instruments

• Accuracy: Closeness to true value. (Absolute Error = Measured - True).

• Precision: Repeatability of readings (clustering). High precision ≠ high accuracy.

• Resolution: Smallest detectable change in input.

• Sensitivity (Scale Factor): Output change per unit input change. For deflection instruments: S = dθ/dx (rad/unit). Static Sensitivity is slope of calibration curve.

• Threshold: Minimum input to cause detectable output.

• Hysteresis: Difference in output for increasing vs. decreasing input.

• Linearity: Maximum deviation from ideal straight-line calibration curve.

• Repeatability: Same conditions, same input → same output.

• Reproducibility: Same input, different conditions (time, operator) → same output.

1.3 Dynamic Characteristics of Instruments

• Concerned with response to time-varying inputs.

• Speed of Response: How fast output follows input.

• Lag: Delay in response (retardation type, time delay type).

• Fidelity: How accurately output reproduces input waveform (shape).

• Dynamic Error: Difference between dynamic output and true instantaneous value.

1.4 Loading Effects & Instrument Loading

• Problem: Connecting a measuring instrument alters the circuit condition.

• Voltmeter Loading: Voltmeter is connected in parallel. Its internal resistance (Rₘ) forms a shunt with the circuit resistance (Rₕ). The measured voltage is lower than the open-circuit voltage.

  Loading Error % = (V_loaded - V_true) / V_true × 100

  For high source resistance (Rₕ), use a voltmeter with high sensitivity (Ω/V) → high Rₘ.

• Ammeter Loading: Ammeter is connected in series. Its internal resistance (Rₘ) adds to the circuit resistance. The measured current is lower than the true current.

  Use an ammeter with very low Rₘ.

• Example: Multimeter on 10V scale with sensitivity 20,000 Ω/V has Rₘ = 200 kΩ. Loading a high-R circuit (e.g., Rₕ = 10 kΩ) causes significant error.

[!TIP] COMMON PITFALL: Always check instrument impedance relative to circuit impedance. For voltage, Rₘ >> Rₕ. For current, Rₘ << Rₕ.

2.0 CLASSIFICATION & OPERATING PRINCIPLES OF ANALOG INSTRUMENTS

2.1 Classification of Analog Instruments

• By Operating Principle:

  • Electromagnetic: PMMC, Moving Iron (MI), Electrodynamic (Dynamometer).

  • Electrostatic: For high voltage AC/DC.

  • Thermal: For RMS of any waveform (thermocouple, thermistor).

  • Electrochemical: pH meters, conductivity.

• By Quantity Measured: Ammeters, Voltmeters, Wattmeters, Energy Meters, etc.

2.2 Permanent Magnet Moving Coil (PMMC) Instruments

• Construction: Permanent magnet (high coercivity steel), cylindrical air gap, moving coil (many turns, aluminum former), spring control (hair-springs), eddy current damping (aluminum frame in magnetic field), pointer, scale.

• Principle: Current in coil → magnetic field interaction with permanent magnet → torque T_d = BINA (B=flux density, I=current, N=turns, A=area). Linear scale because T_d ∝ I.

• Torque Equation: T_d = k₁ I (k₁ = BNA).

• Control Torque: T_c = k₂ θ (spring constant).

• Equilibrium: T_d = T_c → θ ∝ I.

• Applications:

  • Ammeter: Low internal resistance. Shunt required for range extension.

  • Voltmeter: High internal resistance. Series multiplier required.

• Limitations: AC measurement requires rectifier. Sensitive to overload, position.

2.3 Moving Iron (MI) Instruments

• Construction Types:

  • Attraction Type: Single iron piece, coil. Current → iron attracted to coil → movement.

  • Repulsion Type: Two iron vanes (one fixed, one movable) inside coil. Current → both magnetized similarly → repulsion → movement.

• Principle: Non-linear torque. T_d ∝ I² (for both AC & DC). Hence, scale is non-linear (crowded at lower end).

• Torque Equation (Repulsion Type): T_d ∝ (N₁I)² (N₁ = turns on fixed coil). Works for AC/DC without polarity.

• Damping: Air friction damping (vane in air chamber).

• Advantages: Robust, cheap, can measure AC/DC, high overload capacity.

• Limitations: Non-linear scale, low sensitivity, susceptible to stray fields (needs shielding).

2.4 Electrodynamic (Dynamometer) Instruments

• Construction: Two coils:

  • Fixed Coils (Current Coil): Carry current to be measured. Split to allow moving coil movement.

  • Moving Coil (Pressure/Voltage Coil): Carries current proportional to voltage (via series multiplier). Air-cored (no iron).

• Principle: Interaction of magnetic fields from both coils. Torque exists for both AC & DC.

• Torque Equation (AC/DC): T_d = k I₁ I₂ cos φ (I₁ = current coil current, I₂ = pressure coil current, φ = phase angle). For DC, φ=0, T_d ∝ I₁ I₂.

• Scale: Non-linear (√ type) because T_d ∝ I₁ I₂ and for voltmeter/ammeter configurations, one current is fixed or proportional to the other.

• Applications:

  • Wattmeter: (I₁ = load current, I₂ ∝ load voltage).

  • Ammeter/Voltmeter (less common due to low sensitivity).

• Damping: Eddy current damping (moving coil on aluminum frame).

• Special Features for Low Power Factor Wattmeter:

  • High torque design: To overcome low cos φ torque.

  • Compensated pressure coil circuit: Series capacitor to make pressure coil circuit resistive (minimize phase error).

  • Air damping: To avoid hysteresis errors from fluid damping at low PF.

  • Light moving system: For high sensitivity.

3.0 INSTRUMENT TRANSFORMERS (CT & PT)

3.1 Current Transformer (CT)

• Construction: Primary is single turn (conductor or bar). Secondary is multi-turn wound on laminated core. Secondary rated current usually 5A or 1A. Burden = external impedance (Z_b).

• Equivalent Circuit & Phasor Diagram: Similar to a step-down transformer under short-circuited secondary. Key: Exciting current (I₀) has two components:

  • Magnetizing component (Iₘ): Creates core flux.

  • Core loss component (Iₑ): Compensates core loss.

• Ratio Error: n = (Kₙ Iₛ - I₁) / I₁ × 100% (Kₙ = nominal ratio I₁ₙ/Iₛₙ). Caused by exciting current.

• Phase Angle Error (θ): Angle between primary current (I₁) and secondary current reversed (I₂').

• Errors & Minimization:

  • Effect of Exciting Current: Increases ratio error. Minimized by using high permeability core, low flux density.

  • Effect of Secondary Burden (Z_b): Higher Z_b → larger voltage drop in secondary → larger I₀ → larger errors. Keep burden within rated VA.

  • Effect of PF of Primary Current: Affects phase angle error significantly.

• ⚠️ DANGER: Open-Circuited Secondary: No secondary current → all primary current becomes exciting current → extremely high core flux → dangerously high voltage across open secondary terminals → insulation breakdown, safety hazard. Never open CT secondary when primary is energized.

• Testing: Ratio test (compare primary/secondary currents), phase angle test (using zero-phase-factor detector).

3.2 Potential Transformer (PT)

• Construction: Shell-type or core-type. Primary has many turns (for high voltage), secondary few turns (usually 100-110 V). Designed for high accuracy at near-rated burden.

• Equivalent Circuit & Phasor Diagram: Similar to a step-down transformer. Exciting current (I₀) drawn by magnetizing branch.

• Ratio Error: Caused by voltage drop in windings (I₁R₁, I₁X₁, I₂R₂, I₂X₂) and I₀.

• Phase Angle Error: Angle between primary voltage (V₁) and reversed secondary voltage (V₂').

• Errors & Minimization:

  • Effect of Voltage Drop: Minimize by using thick conductors (low R, X).

  • Effect of Burden & its PF: Higher burden or low PF burden → larger voltage drops → larger errors. Operate near rated burden.

  • Effect of Magnetizing Current: Use high permeability core, low flux density.

• Testing: Ratio test (apply known V₁, measure V₂), phase angle test.

3.3 Comparison of CT and PT

4.0 POWER MEASUREMENT - WATTMETERS

4.1 Single-Phase Electrodynamometer Wattmeter

• Construction: Fixed coils (current coil, series with load). Moving coil (pressure coil, series with high resistance multiplier, parallel to load).

• Working Principle: T_d ∝ (Flux from CC) × (Flux from PC) × cos(angle between them).

  • CC flux φ₁ ∝ I₁ (load current).

  • PC flux φ₂ ∝ I₂ (current ∝ load voltage V).

  • Angle between fluxes ≈ phase angle (φ) between V and I (since PC circuit made resistive).

  • Hence, T_d ∝ V I cos φ → Deflection ∝ Real Power.

• Phasor Diagram: Shows V, I, and fluxes. PC current I₂ lags V by small angle α (due to PC inductance).

• Scale: Non-linear (√ type).

• Errors in Electrodynamometer Wattmeter:

  • Stray Magnetic Field Errors: External fields distort CC/PC fluxes → error. Minimized by shielding (iron case).

  • Errors due to Inductance/Capacitance of Pressure Coil: I₂ lags V → T_d ∝ V I cos(φ+α). Error = VI sin φ sin α. Compensated by adding a capacitor in parallel with PC to make PC circuit resistive.

  • Friction, Hysteresis, Eddy Currents: Standard mechanical/electrical errors.

4.2 Special Types of Wattmeters

• Two-Element Wattmeter: Two separate dynamometer elements mounted on same spindle. Used for 3-phase, 3-wire (without neutral). Each element measures power in one phase.

• Three-Element Wattmeter: Three separate elements. Used for 3-phase, 4-wire (with neutral). Each element measures phase power.

• Low Power Factor Wattmeter:

  • High Torque: Light moving system, strong permanent magnets.

  • Compensated Pressure Coil Circuit: Series capacitor to neutralize PC inductance → make PC current in phase with voltage.

  • Air Damping: Avoids fluid hysteresis errors at low PF.

  • Reduced Control Spring Torque: Allows full-scale deflection at low cos φ.

4.3 Three-Phase Power Measurement

• Two-Wattmeter Method:

  • Circuit: Two wattmeters connected in any two lines (say L1, L2). Current coils in two lines, pressure coils from respective lines to third line (L3).

  • Proof (Vector Diagram): W₁ = V₁I₁ cos(30°+φ), W₂ = V₂I₂ cos(30°-φ). For balanced load, V₁=V₂=V_L, I₁=I₂=I_L.

  • Total Power: P = W₁ + W₂ (Algebraic sum).

  • Condition for One Wattmeter Negative: φ > 60° (i.e., PF < 0.5 lagging or > 0.5 leading). One wattmeter reads negative.

• Three Wattmeters: Used for 3-phase, 4-wire (unbalanced). P = W₁ + W₂ + W₃.

5.0 ENERGY MEASUREMENT - ENERGY METERS

5.1 Single-Phase Induction (Kilo-Watt-Hour) Meter

• Construction:

  1. Driving System: Two electromagnets (Voltage Magnet - shunt, Current Magnet - series). Shading band on voltage magnet.

  2. Moving System: Aluminum disc on spindle, in air gap of magnets.

  3. Braking System: Permanent magnet (disc rotates in its field) → eddy currents → braking torque T_b ∝ ω (speed).

  4. Registering System: Gear train & dials (cyclometer or pointer type).

• Working Principle:

  • Voltage flux φ_v (from V magnet, lagging V by ~90° due to shading).

  • Current flux φ_i (from I magnet, in phase with I).

  • Eddy currents induced in disc by φ_v interact with φ_i → driving torque T_d ∝ φ_v φ_i sin θ ∝ V I cos φ.

  • Braking torque T_b ∝ ω.

  • Steady speed: T_d = T_b → ω ∝ V I cos φ → Disc speed ∝ Power.

  • Energy: E = ∫ P dt ∝ ∫ ω dt ∝ Number of revolutions (N).

  • Meter Constant (K): K = N / E (rev/kWh).

• Phasor Diagram: Shows φ_v (lagging V), φ_i (in phase with I), and resultant torque.

• Errors in Energy Meter:

  • Friction: At light loads, T_d may not overcome friction → under-registration.

  • Creeping: Disc rotates with voltage only (no load) due to overcompensation, friction, or stray fluxes. Test: Creep test (V applied, I=0).

  • Braking Magnet: Weak magnet → high speed (under-registration). Strong magnet → low speed (over-registration).

  • Voltage, Frequency, Power Factor Errors: Due to non-ideal characteristics (shading, phase shifts).

  • Self-Braking & Stray Torques: Imperfect design.

• Testing & Calibration:

  • Full Load Test:

    % Error = (Actual Rev - Expected Rev) / Expected Rev × 100

    Expected Rev = (P × t) / (3600 × K) (P in kW, t in sec, K in rev/kWh).

  • Light Load Test: Check friction/creeping.

  • Power Factor Test: At lagging/leading PF.

  • Example (Jun 2025): 50A, 230V meter, K=520 rev/kWh, makes 61 rev in 37 sec.

    P_true = V×I = 230×50 = 11500 W = 11.5 kW

    Expected Rev = (11.5 × 37) / (3600 × 520) = 425.5 / 1872000? Correct Formula: Expected Rev = (P (kW) × t (hr)) × K. t = 37/3600 hr. Expected Rev = 11.5 × (37/3600) × 520 = 61.8 rev. % Error = (61 - 61.8)/61.8 × 100 = -1.3%.

5.2 Three-Phase Energy Meter

• Construction: Either single element with multiple discs (for 3-phase, 3-wire) or multiple elements (two-element for 3-wire, three-element for 4-wire).

• Connection:

  • 3-phase, 3-wire: Two elements, each connected between a line and the other two lines (like two-wattmeter method). Total energy = sum of both elements.

  • 3-phase, 4-wire: Three elements, each between a line and neutral.

5.3 Maximum Demand Meter

• Principle: Measures average power over a fixed interval (e.g., 15 or 30 min). Records the highest such average demand in the billing period.

• Construction: Often a motor-driven integrating meter with a resetting mechanism (thermal or clock-driven). Pointer indicates current demand; maximum demand pointer is latched and resets manually/monthly.

5.4 Digital Electronic Energy Meter

• Block Diagram:

  
  Voltage Sensor (Potential Divider) → ADC → Microcontroller/Processor ← Current Sensor (CT/Shunt)
  
                                                            ↓
  
                                                        Energy Calculation (∫VIdt)
  
                                                            ↓
  
                                                        Display (LCD/LED)
  
                                                            ↓
  
                                                        Memory/Output (Pulse, RS485)
  
  

• Principle: Samples V & I, multiplies instantaneously, integrates over time. Highly accurate, multiple tariffs, tamper-proof.

6.0 SPECIAL PURPOSE INSTRUMENTS & MEASUREMENT TECHNIQUES

6.1 Ballistic Galvanometer

• Construction: Moving coil instrument with very large moment of inertia (heavy coil) and very weak control (long period, T > 5 sec). Critical damping is avoided (underdamped).

• Principle: Measures total charge (Q) passed as a current pulse. The coil receives an impulse → oscillates. First maximum deflection (θ₁) ∝ Q.

• Equation of Motion (for first swing):

  Q = √(4πC K) × θ₁ (for critically damped case, but for BG, damping is small).

  More generally, Q = (C √(K/J)) × θ₁ where C = damping constant, K = control constant, J = inertia.

  Key: θ₁ ∝ Q if damping is constant.

• Calibration: Often done using a known capacitor charged to known voltage.

• Uses: Measure charge, capacitance, magnetic flux linkage.

• Comparison with Flux Meter:

  | Feature | Ballistic Galvanometer | Flux Meter | | :--- | :--- | :--- | | Moving System | Heavy coil, high inertia | Light coil, low inertia | | Damping | Very light (underdamped) | Heavy damping (dead beat) | | Deflection | Proportional to total charge (Q) | Proportional to flux linkage (dΦ/dt) | | Response | Slow (periodic) | Fast, direct reading | | Measurement | Charge, capacitance, flux (via dΦ/dt) | Direct flux measurement |

6.2 Measurement of Magnetic Properties (B-H Curve)

• Method of Reversals:

  1. Specimen (ring or bar) wound with primary (N₁) and secondary (N₂) windings.

  2. Apply slowly increasing DC to primary. At each current I, reverse primary current rapidly.

  3. Integrating voltmeter (ballistic galvanometer) connected to secondary measures ∫e dt = N₂ A ΔB (A = cross-section).

  4. Ballistic deflection θ ∝ ΔB. Plot θ vs. I (∝ H) → hysteresis loop.

  5. Advantage: Eliminates effect of residual magnetism and eddy currents.

• Six-Point Method:

  1. Apply known currents (I₁, I₂, ... I₆) to primary (H ∝ I).

  2. For each I, measure secondary EMF e = N₂ A dB/dt with fluxmeter (not BG).

  3. ΔΦ = ∫ e dt between two points gives ΔB.

  4. Plot B vs. H point by point → dc hysteresis loop.

• Lloyd-Fischer Square Method:

  • Purpose: Measure iron loss (hysteresis + eddy) in a specimen.

  • Setup: Square specimen (lamination) placed in two-coil system (primary for excitation, secondary for induced EMF). Secondary connected to wattmeter.

  • Principle: Wattmeter reading = Core loss × Volume. By knowing dimensions and frequency, calculate core loss per kg.

6.3 Measurement of Resistance

• Wheatstone Bridge:

  • Circuit: Four arms (R₁, R₂, R₃, Rₓ). Galvanometer (G) between junctions, battery across other two.

  • Balance Condition: R₁/R₂ = R₃/Rₓ → Rₓ = R₃ × (R₂/R₁).

  • Used for: Medium resistances (1 Ω to 1 MΩ).

  • Sources of Error:

    • Contact resistance & lead resistance: In series with low Rₓ → error. Minimized by using four-terminal (Kelvin) connections for Rₓ.

    • Thermal EMFs: Dissimilar metal junctions in bridge → stray voltages. Use same metal, reverse battery, average.

    • Bridge sensitivity: Poor galvanometer sensitivity.

• Kelvin's Double Bridge (Thomson Bridge):

  • Purpose: Low resistances (< 1 Ω) where lead/contact resistance matters.

  • Construction: Two pairs of ratio arms (P,Q and p,q). Unknown low resistance (Rₓ) and standard (Rₛ) are four-terminal (separate current and potential leads).

  • Principle: Potential leads of Rₓ and Rₛ connected to points that eliminate effect of lead/resistance (r) of Rₓ and Rₛ.

  • Balance Condition Derivation:

    At balance (G=0), potential at a = potential at c.

    I₁P = I₂p and I₁Q = I₂q → P/Q = p/q = m (say).

    Also, I₁(R + r₁) + I₂Rₛ = I₁Rₓ + I₂(r₂ + r).

    Using current ratios, solving gives:

    Rₓ = Rₛ × (P/Q) + (q/Q) × (r - m r₁)

    If P/Q = p/q (i.e., m = p/q), then Rₓ = Rₛ × (P/Q). The error term vanishes.

  • Superiority: Four-terminal Rₓ, Rₛ eliminate their own lead/contact resistances. Second set of ratio arms cancels remaining lead resistance (r).

• Megger (Insulation Tester):

  • Principle: Hand-cranked or battery-operated high voltage DC source (500V, 1000V, 2500V). Measures very high resistances (MΩ to GΩ).

  • Use: Test insulation resistance of cables, motors, transformers. "Megger" is a trade name, now generic.

6.4 Measurement of Earth Resistance

• Fall-of-Potential (Three-Point) Method:

  1. Earth electrode (E) under test.

  2. Two auxiliary electrodes (P, C) driven in earth, in a straight line, spaced ≥ 20m.

  3. Apply known current I between E and C.

  4. Measure voltage V between E and P.

  5. R = V/I. Move P to find position where V is maximum → that's true earth resistance.

• Four-Point Method: Uses two current and two potential electrodes, eliminates effect of connecting lead resistances.

• Earth Tester: Portable instrument with hand-driven generator, voltage/current meters, and terminals for electrodes. Shows direct reading.

6.5 Frequency Meters

• Resonant (Vibrating Reed): Tuned reeds resonate at specific frequencies. Visual indication.

• Weston (Electrodynamometer) Type: Two fixed coils (reactive & resistive), moving coil. Deflection ∝ frequency.

• Digital Frequency Meter:

  • Block Diagram:

    
    Signal → Shaper (Schmitt trigger) → Gate (controlled by time base) → Counter → Display
    
    

  • Principle: Counts number of cycles of input signal in a precise time interval (1 sec, 0.1 sec) generated by crystal oscillator. f = Count / Gate time.

6.6 Ratio Meters

• Purpose: Measure ratio of two quantities (e.g., voltage ratio in PT, current ratio in CT, impedance ratio).

• Principle: Often use two dynamometer elements on same shaft. One element's torque ∝ I₁², other's ∝ I₂². Net deflection ∝ (I₁² - I₂²) or difference. Balanced when I₁ = I₂.

• Use: CT/PT testing, impedance measurement.

7.0 INSTRUMENT DAMPING, RANGE EXTENSION & CALIBRATION

7.1 Damping Methods

• Purpose: Bring pointer to rest quickly without oscillation.

• Air Friction Damping: Piston in air chamber (PMMC, MI). Works in any position.

• Eddy Current Damping: Most common. Moving conductor (aluminum frame) in magnetic field → eddy currents → opposing torque. Used in PMMC, Dynamometer. Requires permanent magnet.

• Fluid Friction Damping: Vane in oil. High damping, but position-sensitive, messy.

• Electromagnetic (Electrical) Damping: Short-circuiting moving coil (in PMMC) or using a separate damping coil.

7.2 Range Extension of Instruments

• Ammeter Range Extension (Shunt):

  Let I = full-scale current, Iₘ = meter current, Rₘ = meter resistance.

  Shunt Rₛ carries Iₛ = I - Iₘ.

  Rₛ = (Iₘ Rₘ) / (I - Iₘ)

  Multi-range ammeter: Multiple shunts with rotary switch.

• Voltmeter Range Extension (Series Multiplier):

  Let V = full-scale voltage.

  Rₛ must drop V - Vₘ where Vₘ = Iₘ Rₘ.

  Rₛ = (V - Vₘ) / Iₘ = (V/Iₘ) - Rₘ

  Multi-range voltmeter: Multiple series resistors with rotary switch. Use high-voltage multiplier for very high ranges.

7.3 Testing & Calibration of Instruments

• Procedure: Compare instrument reading with a standard of higher accuracy (potentiometer, standard cell, calibrated reference meter).

• Errors Determination:

  • Absolute Error (e): e = X_measured - X_true

  • Relative Error (ε): ε = e / X_true

  • Percentage Error: %e = (e / X_true) × 100 or (e / Full Scale) × 100 (for instruments).

• Example (Calibration): Use a potentiometer to provide precise voltage/current. Compare readings. Plot calibration curve (error vs. reading).

• Ammeter/Voltmeter Calibration: Use standard shunt/resistor and precise voltmeter to measure voltage drop across known resistance → calculate true current. Or use potentiometric method.

[!TIP] EXAM TIP: Always specify whether % error is based on true value or full-scale deflection (FSD). In energy meter full-load test, it's based on expected revolutions (true power).