The energy meter reads exactly one third of the logged consumption
A workshop is billed on a 415 V, three-phase, four-wire static energy meter connected through three 400/5 A current transformers; the voltage circuits are connected directly, with no PTs. Over a 30-day billing period the meter dial advanced by 480 units. The workshop's own production logger, which records the running load separately, shows 8 hours per day at 220 kW and 16 hours per day at 130 kW for all 30 days. Measured line currents during the audit are 201 A, 202 A and 200 A at 130 kW, and 340 A, 341 A and 339 A at 220 kW; the phase voltages are balanced. The meter seal is intact, the meter has a valid calibration certificate, and the consumer disputes the bill. The accountant's first instinct is to multiply the whole year's consumption by three and raise a supplementary bill.
1. Compute the metering multiplier, the energy actually registered, and the energy the load log implies. Express the shortfall as a percentage.
Read the worked answer
Multiplier. With no PTs, the multiplier is the CT ratio alone: 400/5 = 80. (If PTs were present it would be 80 × PT ratio.)
Registered energy = dial advance × multiplier = 480 × 80 = 38,400 kWh.
Energy implied by the load log:
- Daily = (8 h × 220 kW) + (16 h × 130 kW) = 1760 + 2080 = 3840 kWh/day.
- For 30 days = 3840 × 30 = 115,200 kWh.
Shortfall = 115,200 − 38,400 = 76,800 kWh, i.e. 66.7% under-registration, and the ratio is exactly 3.000.
Why the multiplicand checks out independently: at 130 kW and 0.9 power factor, current = 130,000 / (1.732 × 415 × 0.9) ≈ 201 A, matching the measured currents; at 220 kW it is ≈ 340 A, also matching. So the CTs are not saturated and the load log is credible. The currents also confirm the load is effectively balanced, which matters for the next step.
A near-exact factor of three on a balanced load is a diagnostic fingerprint, not a random failure. The accountant's instinct to multiply by three is arithmetically right for this period but wrong as a billing action across a year.
2. Which single defect produces exactly one-third registration on this metering arrangement, and why do the obvious alternatives not fit?
Read the worked answer
The fit: one CT secondary reversed at the meter terminals. In a three-element, four-wire meter, total power is the algebraic sum of the three elements: P = P1 + P2 + P3. With a balanced load each element reads P/3. Reverse one CT's secondary and that element reads −P/3, so the meter registers P/3 + P/3 − P/3 = P/3 - exactly one third, independent of load level. That matches the observed 3.000 ratio precisely.
Why the alternatives fail:
- One CT secondary open or shorted: that element reads zero, giving 2P/3 - a ratio of 1.5, not 3.
- One voltage phase missing in a three-element meter: approximately two elements contribute, again near 2P/3.
- Wrong CT ratio used (e.g. 600/5 CTs billed as 400/5): ratio 1.5, wrong direction and wrong magnitude.
- Wrong multiplier applied: gives a factor of 2, 4 or 10 depending on the error, not a clean 3, and would not depend on the load being balanced.
- Meter calibration drift: drifts by a few percent; a 67% error is not drift.
The balanced currents (200–202 A and 339–341 A) are what make the one-third signature clean. On an unbalanced load the same defect gives a factor that varies with the load pattern, which is why the auditor should check whether the ratio was exactly 3 in earlier periods too.
3. Describe how you would confirm the defect on site, how the wiring should be corrected, and what period the supplementary bill may legitimately cover.
Read the worked answer
Confirmation. Use a portable three-phase power analyser or a reference check meter with its own clamps and voltage leads, and compare element by element with the meter's own per-phase power readings. A reversed CT shows up as a negative element power or a phase angle near 180° between that CT secondary current and its phase voltage. Confirm the CT polarity physically: P1 must face the supply side, S1 must go to the meter's incoming terminal for that phase, and the three CTs must be identically oriented.
Correction, safely. Never open-circuit a live CT secondary - the secondary can develop a dangerous voltage across the open circuit and flash over. Short the CT secondary at a test terminal block first, then rewire with the circuit isolated, remove the short, and restore. After restoration, run a load test: compare the meter's kWh increment against the analyser over at least one hour at a steady load; agreement within about ±1% closes the job. Re-seal and record.
Billing period. The correction factor may only be applied to the period during which the defect provably existed - normally back to the last meter inspection, sealing or calibration date, or the last recorded reading that was consistent with the load log. Multiplying a whole year by three without evidence is not defensible. Attach the audit readings, the analyser printout and the correction certificate to the bill.