Measurement of energy and energy meters

Why it matters

Every unit of electricity sold is counted by an energy meter, so a 1 % error in a meter is a 1 % error in someone's bill. Testing meters against a standard, interpreting meter constants and understanding why an induction meter creeps or reads wrong at low power factor are routine tasks for metering and utility engineers, and favourite numericals.

Key ideas

Energy is power integrated over time, E = ∫p dt. The commercial unit is the kilowatt-hour: 1 kWh = 3.6 MJ. An energy meter is an integrating instrument: it totals energy rather than indicating instantaneous power.

Induction-type (electromechanical) energy meter — four systems.

• Driving system: a series magnet (few turns of thick wire, carries load current, flux ∝ I) and a shunt magnet (many turns, connected across the supply, highly inductive, flux ∝ V and lagging V by nearly 90°). The two alternating fluxes pass through an aluminium disc and induce eddy currents. Each flux reacts with the eddy currents of the other, producing a net driving torque Td ∝ V·I·sin Δ, where Δ is the phase angle between the two fluxes.
• Lag adjustment: copper shading bands or a lag coil on the shunt magnet are adjusted so that the shunt flux lags V by exactly 90°. Then Δ = 90° − φ and Td ∝ VI cos φ, i.e. proportional to true power.
• Moving system: a light aluminium disc on a spindle with jewel bearings.
• Braking system: a permanent magnet near the disc edge. The disc cutting its field induces eddy currents giving a braking torque proportional to speed. In steady state driving = braking torque, so speed ∝ power and revolutions ∝ energy. Moving the brake magnet radially adjusts the full-load speed.
• Registering (counting) mechanism: gear train and dials or a cyclometer register reading kWh.

Adjustments and errors.

• Friction compensation (light-load adjustment): a small shading vane gives a small extra driving torque, independent of load, to overcome friction at light load.
• Creep: slow continuous rotation with the potential coil energised and no load, caused by over-compensation or supply over-voltage. It is prevented by two small holes drilled diametrically opposite in the disc, or a small iron piece on the spindle attracted by the brake magnet.
• Overload compensation: magnetic shunts in the series magnet, because at high current the series flux causes self-braking.
• Phase (lag) error: if Δ is not exactly 90° − φ, the meter is correct at unity power factor but in error at low power factor.
• Temperature: changes in disc and coil resistances and in magnet strength.

Meter constant. The number of revolutions (or LED pulses for an electronic meter) per kWh, marked on the nameplate, e.g. 1200 rev/kWh or 3200 imp/kWh. The registered energy is revolutions ÷ constant.

Testing. The meter is run at a known load for a timed interval and compared with a standard (substandard) meter or wattmeter-and-stopwatch. Phantom (fictitious) loading supplies the current and pressure circuits from separate low-voltage and normal-voltage sources so that a large current can be tested without dissipating the full power. Error is quoted as (registered − true)/true × 100; accuracy classes (e.g. class 1.0) are set by the relevant standard.

Electronic (static) meters sample voltage and current, multiply digitally to get instantaneous power, integrate, and output pulses whose rate is proportional to power. They have no moving parts, no creep, wide range, and can record maximum demand, time-of-day tariffs and import/export energy. Three-phase meters use two elements (3-wire) or three elements (4-wire), following Blondel's theorem.

Formulas

E = P·t ; 1 kWh = 3.6 × 10⁶ J P = average power (kW); t = time (h).

P = V·I·cos φ (single-phase load, W)

E_registered = N / K ; E_true = V·I·cos φ·t / 3.6 × 10⁶ (kWh, t in s) N = revolutions (or pulses) counted; K = meter constant (rev/kWh or imp/kWh).

% error = (E_registered − E_true) / E_true × 100

Td ∝ V·I·sin(Δ_v − φ) Δ_v = angle by which the shunt-magnet flux lags V (ideally 90°); φ = load phase angle (lagging positive). With Δ_v = 90°, Td ∝ VI cos φ.

Speed (rev/h) = K × P(kW)

Worked examples

Example 1 — testing a meter. A single-phase meter with constant 2400 rev/kWh is tested at 230 V, 5 A, unity power factor. The disc makes 60 revolutions in 80 s. Find the percentage error.

1. True power P = 230 × 5 × 1 = 1150 W.
2. True energy in 80 s: E_true = 1150 × 80 / 3.6 × 10⁶ = 0.025556 kWh.
3. Registered energy: E_reg = 60 / 2400 = 0.025 kWh.
4. % error = (0.025 − 0.025556) / 0.025556 × 100 = −2.17 %.

Answer: the meter runs slow by 2.17 %. (A correct meter would make 61.3 revolutions.)

Example 2 — lag-adjustment error (GATE level). In an induction meter the shunt-magnet flux lags the voltage by 88° instead of 90°. The meter is correct at unity power factor. Find its percentage error at 0.5 power factor lagging.

1. Td ∝ VI sin(Δ_v − φ). At upf (φ = 0) the meter reads VI sin 88° = 0.99939 VI; calibration makes this read VI, so the scale factor is 1/0.99939.
2. At pf 0.5 lagging, φ = 60°: Td ∝ VI sin(88° − 60°) = VI sin 28° = 0.46947 VI.
3. Reading = 0.46947/0.99939 = 0.46976 VI; true value = 0.5 VI.
4. % error = (0.46976 − 0.5)/0.5 × 100 = −6.05 %.

Answer: the meter reads about 6.05 % low at 0.5 pf lagging, although it is correct at unity pf — this is why lag adjustment is done at low power factor.

Example 3 — disc speed. A 1800 rev/kWh meter carries 230 V, 10 A at unity power factor. Find the disc speed.

1. P = 2.3 kW; rev/h = 1800 × 2.3 = 4140; rpm = 4140/60.

Answer: 69 rpm.

Common mistakes

• Forgetting to convert seconds to hours (or J to kWh, factor 3.6 × 10⁶).
• Defining error with the true value in the numerator; error = registered − true, so a slow meter has a negative error.
• Assuming the shunt flux lags V by exactly 90° by itself — it needs the lag adjustment; without it the meter errs at low pf.
• Confusing creep (rotation at no load) with friction error (slow running at light load).
• Taking the meter constant as kWh per revolution instead of revolutions per kWh.

For GATE IN

Expect NAT questions on meter constants, the percentage error from a timed test, disc speed and the error caused by imperfect lag adjustment at a given power factor. MCQs test the purpose of the brake magnet, lag adjustment, creep holes, light-load compensation and phantom loading. Practise the units chain W → kWh → revolutions quickly and accurately.

Quick check

1. A 3200 imp/kWh electronic meter flashes 32 times. How much energy was registered?
2. What is creep and how is it prevented?
3. Which component makes disc speed proportional to power?
4. A 1200 rev/kWh meter on a 1.5 kW load: revolutions in 2 minutes? Answers: 1. 0.01 kWh (10 Wh); 2. rotation with no load current; two holes drilled diametrically opposite in the disc (or an iron tag on the spindle); 3. the permanent brake magnet (braking torque ∝ speed); 4. 1200 × 1.5 × 2/60 = 60 revolutions.