Single-phase electrodynamometer wattmeter

The electrodynamometer wattmeter measures power in DC and single-phase AC circuits. It works on the principle that a current-carrying coil placed in the magnetic field of another current-carrying coil experiences a torque.

Construction

  Fixed coils (current coil, 2 sections, thick wire, low R)
        ____         ____
       |    |  /|\  |    |
 load ->|CC  |  | | |  CC |-> to load
       |____| spindle|____|
              moving coil (pressure coil, thin wire)
              + series high resistance R

• Fixed coils (current coils): two identical coils of a few turns of thick wire, connected in series with the load and carrying the load current I. Using two coils gives a nearly uniform field.
• Moving coil (pressure/voltage coil): many turns of fine wire, pivoted between the fixed coils and connected across the load voltage in series with a high non-inductive resistance R; it carries a current ∝ V.
• Control: springs (which also lead the current into the moving coil); damping: air friction; a pointer and scale; and shielding with high-permeability material against stray fields.
• The scale is nearly uniform when properly designed.

Working

The load current flows in the fixed coils and produces a field proportional to it. The moving coil carries a current proportional to the voltage. The interaction produces a deflecting torque proportional to the product of the two currents, i.e. to the power.

Deflection for AC operation

Let the supply voltage be v = Vm sin ωt and the load current (through the fixed coils) be i1 = Im sin(ωt − φ), where φ is the load phase angle. The pressure-coil circuit is taken as purely resistive (its inductance is negligible), so its current is i2 = v/Rp = (Vm/Rp) sin ωt, where Rp is the total resistance of the pressure branch.

Instantaneous torque: Td(inst) = i1 i2 (dM/dθ), where M is the mutual inductance between the coils.

Mean torque over one cycle:

Td = (dM/dθ) · (1/T)∫₀ᵀ i1 i2 dt = (dM/dθ) · (Im Vm/ Rp) · ½ cos φ

With rms values I and V:

Td = (V I cos φ / Rp) (dM/dθ)

At equilibrium, the controlling torque of the spring, Tc = Kθ, equals Td:

θ = (1/K) (V I cos φ / Rp) (dM/dθ) = (P/ (K Rp)) (dM/dθ)

If dM/dθ is nearly constant over the working range, θ ∝ P = V I cos φ, so the deflection is proportional to the average power and the scale is uniform.

Errors: pressure-coil inductance, capacitance of the series resistor, eddy currents, stray fields and temperature. They are reduced by compensation (a capacitor across part of R) and by shielding.