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.

OVERCURRENT PROTECTION OF POWER TRANSFORMER BASIC INFORMATION

Effects of Overcurrent.
A transformer may be subjected to overcurrents ranging from just in excess of nameplate rating to as much as 10 or 20 times rating. Currents up to about twice rating normally result from overload conditions on the system, while higher currents are a consequence of system faults.

When such overcurrents are of extended duration, they may produce either mechanical or thermal damage in a transformer, or possibly both. At current levels near the maximum design capability (worst-case through fault), mechanical effects from electromagnetically generated forces are of primary concern.

The pulsating forces tend to loosen the coils, conductors may be deformed or displaced, and insulation may be damaged. Lower levels of current principally produce thermal heating, with consequences as described later on loading practices. For all current levels, the extent of the damage is increased with time duration.

Protective Devices. 
Whatever the cause, magnitude, or duration of the overcurrent, it is desirable that some component of the system recognize the abnormal condition and initiate action to protect the transformer. Fuses and protective relays are two forms of protective devices in common use.

A fuse consists of a fusible conducting link which will be destroyed after it is subjected to an overcurrent for some period of time, thus opening the circuit. Typically, fuses are employed to protect distribution transformers and small power transformers up to 5000 to 10,000 kVA.

Traditional relays are electromagnetic devices which operate on a reduced current derived from a current transformer in the main transformer line to close or open control contacts, which can initiate the operation of a circuit breaker in the transformer line circuit. Relays are used to protect all medium and large power transformers.

Coordination.
All protective devices, such as fuses and relays, have a defined operating characteristic in the current-time domain. This characteristic should be properly coordinated with the current-carrying capability of the transformer to avoid damage from prolonged overloads or through faults.

Transformer capability is defined in general terms in a guide document, ANSI/IEEE C57.109, Transformer Through Fault Current Duration Guide. The format of the transformer capability curves is shown in Fig. 10-35.

The solid curve, A, defines the thermal capability for all ratings, while the dashed curves, B (appropriate to the specific transformer impedance), define mechanical capability. For proper coordination on any power transformer, the protective-device characteristic should fall below both the mechanical and thermal portions of the transformer capability curve.

(See ANSI/ IEEE C57.10-38 for details of application.)