Electrodynamometer Type Instruments - GATE Notes & Videos for Electrical Engineering

Introduction

The electrodynamometer is a transfer-type instrument. A transfer-type instrument is one that may be calibrated with a DC source and then used without modification to measure AC; this requires the instrument to have the same accuracy for both DC and AC. Electrodynamometer instruments are therefore also called electrodynamic or dynamometer-type instruments.

An electrodynamometer is a moving-coil instrument in which the operating magnetic field is produced by another fixed coil rather than by a permanent magnet. The instrument can be used as an ammeter or a voltmeter, but it is most commonly used as a wattmeter for measurement of electrical power.

The moving coil experiences torque in the field produced by the fixed coils. If the direction of the field reverses together with the current in the moving coil, the torque remains unidirectional for both halves of an AC cycle; this property enables accurate AC measurements.

Electrodynamometer or Electrodynamic instrument

Basic functional parts

• Fixed coils (field coils) that produce the operating magnetic field.
• Moving coil which rotates in the field and carries the quantity to be measured (or a proportion of it).
• Control springs that provide the controlling torque and also act as current leads to the moving coil.
• Moving system including spindle, counterweights and pointer or suspension for sensitive instruments.
• Damping arrangement (normally air-friction vanes) to prevent oscillation of the pointer.
• Shielding or magnetic screens to reduce errors due to stray magnetic fields.
• Case and scale which support and display the instrument reading.

Working principle of electrodynamometer instruments

The basic physical principle is magnetic interaction between currents. Two coils (one fixed and one movable) carry currents. The mutual inductance between these coils depends on the angular position of the moving coil. Energy interchange between electrical and magnetic fields produces mechanical work (torque) that turns the moving coil.

• If a permanent-magnet moving-coil instrument is fed with AC, the torque reverses each half-cycle and the pointer cannot follow rapid reversals; the result is no useful reading for ordinary supply frequencies.
• In an electrodynamometer the field itself is produced by current (through fixed coils) and can be connected so that the field polarity reverses simultaneously with the current in the moving coil. The product of the two currents then gives a unidirectional torque (proportional to the mean of the instantaneous product over a cycle).
• The moving system, because of inertia and damping, responds to the average (mean) torque and indicates a steady deflection proportional to this average.

Why PMMC instruments cannot be used for AC measurements

• PMMC (permanent-magnet moving-coil) instruments depend on a fixed magnetic field produced by a permanent magnet. When AC is applied the torque alternates and the pointer cannot follow the rapid alternations-resulting in near-zero net deflection at power frequencies.
• For AC measurement the magnetic field in the air gap must vary synchronously with the measured current so that the instantaneous torque does not change sign; this is achieved in electrodynamometer instruments by using current-driven fixed coils instead of a permanent magnet.

Construction details

This section expands on the principal parts listed earlier, describing constructional and material choices made to improve accuracy and reduce errors.

Fixed coils

• The operating field is produced by a fixed coil or by two symmetrical fixed coils to give a more uniform field near the centre and to allow passage of the instrument spindle.
• For small-current applications (milliammeter/voltmeter use) fixed coils are wound with fine wire. For ammeters and wattmeters the fixed coils are wound with heavy wire so they carry the main current.
• Where necessary, conductors are stranded to reduce eddy-current losses. Coils are varnished and baked to form a rigid assembly and then clamped to rigid supports to avoid dimensional changes that would affect calibration.
• Non-conducting or ceramic supports are preferred; metallic supports can give rise to eddy currents and weaken the field.

Moving coil

• The moving coil is either self-supporting or wound on a non-metallic former. A metallic former is avoided because eddy currents would be induced in it by alternating flux.
• The moving coil and fixed coils are normally air-cored (no ferromagnetic core) to reduce hysteresis and core losses and to keep the device linear for DC and AC.
• Light but rigid construction is used to keep inertia low while maintaining mechanical stability and reproducible geometry.

Control

• Two hairsprings provide the controlling torque, bring the moving coil back to zero and serve as electrical leads to the moving coil. The spring constant determines control torque T_c = kθ for small deflections.

Moving system

• The moving coil is mounted on a spindle (aluminium or non-magnetic material). The moving system carries counterweights and the pointer; suspension may be used for very high sensitivity instruments.

Damping

• Damping is normally by air-friction using aluminium vanes attached to the spindle and moving in sector-shaped chambers; this prevents long oscillations and enables quick settling to steady deflection.

Shielding

• The operating magnetic field produced by the fixed coils is relatively weak (typically about 0.005 to 0.006 Wb/m²). External magnetic fields, including the earth field, can significantly affect readings.
• To reduce stray-field errors, electrodynamometer movements are enclosed in cases or shields of high-permeability alloy which divert external flux away from the coils.

Cases and scales

• Laboratory standard instruments are often mounted in polished wooden cases dimensionally stable over long periods. The window glass may be coated with a conducting film to reduce electrostatic effects.
• Levelling screws and a spirit level are provided so that the instrument can be accurately levelled during calibration and use.

Torque and energy relations

Define the following quantities:

i₁ = instantaneous current in fixed coils (A)

i₂ = instantaneous current in moving coil (A)

L₁ = self-inductance of fixed coils (H)

L₂ = self-inductance of moving coil (H)

M = mutual inductance between fixed and moving coils (H), which depends on the angular position θ of the moving coil.

Flux linkage of coil 1:

ψ₁ = L₁ i₁ + M i₂

Flux linkage of coil 2:

ψ₂ = L₂ i₂ + M i₁

Electrical input energy in a small time dt is:

i₁ dψ₁ + i₂ dψ₂

Energy stored in the magnetic field is:

W = ½ L₁ i₁² + ½ L₂ i₂² + M i₁ i₂

Change in stored energy is:

dW = ½ i₁² dL₁ + ½ i₂² dL₂ + i₁ i₂ dM + terms from di₁, di₂

Assuming self-inductances L₁ and L₂ are constant with position, dL₁ = dL₂ = 0. From energy conservation, the mechanical work done (dW_m) is the difference between electrical input energy and change in stored magnetic energy, giving:

dW_m = i₁ i₂ dM

If T_i is instantaneous torque and dθ is a small angular displacement, then mechanical work is:

T_i dθ = i₁ i₂ dM

Therefore the instantaneous torque is:

T_i = i₁ i₂ (dM/dθ)

Operation with DC

For DC magnitudes I₁ and I₂, the steady deflecting torque is:

T_d = I₁ I₂ (dM/dθ)

The controlling torque provided by the spring is T_c = k θ, where k is the spring constant (N·m per radian). At steady equilibrium:

I₁ I₂ (dM/dθ) = k θ

If the coils are connected in series to measure current, I₁ = I₂ = I, so:

θ = (I²/k) (dM/dθ)

Thus for DC the deflection is proportional to the square of the current, which makes the scale non-uniform and crowded at the ends.

Operation with AC

Let i₁(t) and i₂(t) be the instantaneous currents in the fixed and moving coils respectively. Instantaneous torque is:

T_i(t) = i₁(t) i₂(t) (dM/dθ)

If the coils are in series for current measurement then i₁(t) = i₂(t) = i(t) and:

T_i(t) = i(t)² (dM/dθ)

The moving system cannot follow rapid instantaneous variations; it responds to the average (mean) torque over one period T:

T_d = (dM/dθ) (1/T) ∫₀^T i(t)² dt

At steady position, the average deflecting torque equals the control torque T_c, and therefore the steady deflection is proportional to the mean of the square of the current. If the scale is calibrated in terms of the square root of this mean-square quantity, the instrument directly reads the RMS value of the AC quantity.

Sinusoidal currents with phase displacement

For sinusoidal currents displaced by a phase angle φ:

i₁ = I_m1 sin ωt

i₂ = I_m2 sin(ωt - φ)

The average deflecting torque over one period is proportional to:

(dM/dθ) × (I₁ I₂ cos φ)

where I₁ and I₂ are RMS values of the currents. Thus the deflection depends on the product of RMS currents and the cosine of phase difference; if the coils carry proportional currents and one coil is arranged to be in phase with voltage, the instrument can measure power (average VI cos φ).

Types of electrodynamometer instruments

• Electrodynamic ammeter
• Electrodynamic voltmeter
• Electrodynamic wattmeter

Electrodynamic ammeter

In an electrodynamic ammeter the fixed and moving coils are connected in series. A shunt is normally connected across the moving coil to limit the current through it for practical sensitivity and to protect the hairsprings.

Electrodynamometer ammeter

The reactance-to-resistance (X/R) ratio of the shunt and moving-coil circuit is chosen so that the instrument reading remains nearly independent of supply frequency. Deflecting torque is proportional to the mean-square current when coils are in series; the scale is therefore calibrated to read the RMS value.

Electrodynamic voltmeter

An electrodynamometer can be used as a voltmeter by connecting a large non-inductive resistor R in series with the moving coil so that the current in the coil is proportional to the applied voltage (and nearly in phase with it). The instrument then responds to the mean square of that coil current and, after calibration, gives the RMS voltage.

Electrodynamometer voltmeter

Electrodynamic wattmeter

The electrodynamic wattmeter has two fixed coils and one movable coil. The fixed coils (current coils) are placed symmetrically to produce a uniform field and are connected in series with the load so that their current is proportional to load current.

Electrodynamometer wattmeter

The moving coil is connected in series with a high non-inductive resistance R_v (voltage coil) and is connected across the supply so that its current is proportional to supply voltage and practically in phase with it. The instantaneous torque is proportional to the instantaneous product of current in the current coils and current in the voltage coil, which is proportional to instantaneous power. The moving coil is mounted on a pivoted spindle that carries the pointer; hairsprings provide control torque and current leads; air friction provides damping.

Basic Arrangement of an Electrodynamometer Wattmeter

Wattmeter torque relation and power measurement

Let i_f be current in fixed (current) coils and i_m be current in moving (voltage) coil. Let v and i denote load voltage and load current respectively.

Instantaneous torque is proportional to the instantaneous product of the coil currents:

T_in ∝ i_f i_m

Since i_f ∝ i (current coil proportional to load current) and i_m ∝ v (voltage coil proportional to supply voltage),

T_in ∝ v i ∝ instantaneous power p(t)

Because the moving system responds to the average torque, the instrument reads the average (true) power. For sinusoidal quantities:

v = V_m sin ωt

i = I_m sin(ωt - φ)

The average torque is proportional to V I cos φ, i.e. the true active power P. With spring control T_c = k_s θ₁ and at equilibrium T_c = T_d, so θ₁ ∝ P and the wattmeter scale is uniform.

Advantages of electrodynamometer instruments

• Suitable for both AC and DC measurements with similar calibration.
• Free from eddy-current and hysteresis errors associated with iron cores, since coils are commonly air-cored.
• Accurate measurement of RMS values of voltage or current irrespective of waveform shape.
• Being a transfer-type instrument, it is useful as a standard/calibration instrument where the same calibration for AC and DC is required.

Disadvantages of electrodynamometer instruments

• Because the response for current measurement in the series-connected case is proportional to I², the scale is non-uniform for direct-current measurement without re-scaling.
• Low torque-to-weight ratio-moving coil must have many turns to produce sufficient mmf, but that increases weight and reduces the torque/weight ratio, increasing frictional errors.
• More expensive than PMMC and moving-iron instruments.
• Requires adequate screening against stray magnetic fields because the operating field is weak.
• Relatively higher power consumption in the coil circuits compared with some other instrument types because coils must carry significant currents.

Sources of error and remedies

Common errors in electrodynamometer instruments and their practical remedies are:

• Low torque-to-weight ratio: A heavy moving coil reduces the torque/weight ratio and increases frictional errors. Remedy: use lightweight, rigid materials for the moving system and optimise number of turns and current; reduce friction at bearings.
• Frequency errors: Self-inductance of coils causes impedance to change with frequency, altering the currents in fixed and moving circuits and hence the torque. Remedy: design the fixed and moving coil circuits to have nearly equal time constants or use compensation networks so the meter reading is nearly independent of supply frequency.
• Eddy-current errors: Metallic parts near alternating flux induce eddy currents which distort the field and torque. Remedy: minimimise metal parts near coils, make metallic parts from high-resistivity or laminated materials, and use non-conducting supports where possible.
• Stray magnetic field errors: Weak operating field makes the instrument sensitive to external fields. Remedy: magnetic shielding using high-permeability enclosures and careful orientation during calibration.
• Temperature errors: Self-heating of coils changes resistance and thus current distribution. Remedy: use temperature-compensating resistors or materials with low temperature coefficients and ensure adequate thermal design.

Range and typical ratings

Typical practical ranges for electrodynamometer instruments are:

• Ammeter: with fixed coil and moving coil in series typical low-range rating ≈ 200 mA; with moving coil shunted (to extend range) up to ≈ 30 A.
• Voltmeter: voltmeter ranges possible up to about 750 V (using appropriate high non-inductive series resistance and insulation).

Comparison with other instrument types

Electrodynamometer instruments combine advantages of being usable on both DC and AC and giving true-RMS or true-power readings, but trade off higher cost and lower torque/weight ratio when compared with PMMC and moving-iron instruments.

Applications and practical notes

• Precision power measurement: Electrodynamometer wattmeters are used as laboratory standards and in calibration work where true active power measurement is required for AC and DC.
• Transfer standard: Because they can be calibrated with DC and used for AC without change, electrodynamometer instruments serve as transfer standards between DC and AC calibrations.
• Waveform independence: Air-cored electrodynamometer voltmeters and ammeters can measure RMS values accurately even for non-sinusoidal waveforms if the moving and fixed coil circuits are designed appropriately.
• Practical installation: Ensure instruments are levelled during calibration and use, shields are installed to avoid stray-field errors, and thermal conditions are controlled to reduce temperature errors.

Summary

The electrodynamometer (dynamometer-type) instrument is an essential precision instrument class for measuring RMS current, RMS voltage and true power for both AC and DC. Its operation is based on interaction of currents in fixed and moving coils; torque depends on the product of coil currents and the rate of change of mutual inductance with angle. Proper construction, shielding and compensation reduce the principal errors and make these instruments suitable for laboratory and calibration use.