POWER AND ENERGY EFFICIENCIES OF TRANSFORMERS BASIC INFORMATION


The nominal power efficiency ηpower of a transformer is the ratio of rated real power output to rated real power input: ηpower = Pout/Pin = 1− (Ploss/Pin). Total losses Ploss are the sum of the no-load and load losses. No-load losses consist of eddy-current and hysteresis losses within the core (|˜ic|2 Rc, the loss caused by the core-loss component ic of the exciting current iφ;), ohmic loss |˜iφ|2 Rp, and dielectric loss: that is, all losses that occur at full voltage with the secondary circuit open.

Load losses are |˜ip(t)|2 Rp+|˜is(t)|2 Rs caused by the primary [ip(t)] and secondary [is(t)] load currents. Eddy-current losses also occur, induced by stray fluxes within the solid transformer structure, and similar losses are generated in the windings, varying with the load current.

No-load losses are measured at rated frequency and rated secondary voltage (if the secondary side is the low-voltage side) and are considered to be independent of load. Load losses are measured at rated frequency and rated secondary current, but with the secondary short-circuited and with reduced voltage applied to the primary, the high-voltage side. Load losses can be assumed to vary as the square of the load current.

Most units are not fully loaded all the time, and therefore one defines the energy efficiency of a transformer, where lightly loaded periods are also taken into account during a load cycle. For low-power-efficiency transformers (ηpower < 96%) the loss can be measured from the relatively large difference between the input power Pin and the output power Pout.

However, for high power efficiency units (ηpower > 96%), the errors in measuring Pin and Pout and the small difference between the two make an efficiency determination meaningless. If two current transformers (CTs, maximum errors εCT1 = εCT2 = 5 mA, CT ratio = 20) and two potential transformers (PTs, εPT1 = εPT2 = 0.24 V, PT ratio = 30) as well as two ammeters (εA1 = εA2 = 5 Ma) and voltmeters (εV1 = εV2 = 0.3 V) with full-scale errors of 0.1% are used, then the maximum error in the measured losses for a 25 kVA, ηpower = 98.44%, 240 V/7200 V single-phase transformer at cos φ1 = 1 is #Ploss = (240 V ± εPT1 ± εV1)(5.20835 A ± εCT1 ± εA1) × 20 − 30 (240 V ± εPT2 ± εV2 (3.472 A ± εCT2 ± εA2) = (240.54 V) × (104.367 A) − (7183.8 V) × (3.462 A) = 234.1 W, so that #Ploss/Ploss = ± (234.1/390)100% ≈ 60%.

This means the conventional method of measuring the losses and therefore the power efficiency of high-efficiency units does not produce accurate results, and other methods must be used.

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