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Transformer Condition for maximum Efficiency

Transformer Efficiency All day Efficiency & Condition for maximum Efficiency Table of Contents Efficiency of Transformer Formulas for Transformer Efficiency Condition for Maximum Efficiency of Transformer All Day Efficiency of Transformer Efficiency of Transformer Transformer efficiency may be defined as the ratio between Output and Input. Transformer Efficiency = Output / Input On specified power factor and load, the transformer efficiency can be found by dividing its output on Input (similar to other electrical machines i.e. motors, generators etc). But the values of both Input and Output should be same in unites (i.e. in Watts, kilowatts, megawatts etc) But note that a transformer has very high efficiency because the losses occur in transformer are very low. Since the Input and Output almost equal, therefore measurement of input and output is practically not possible. The best way to find the transformer efficiency is that, first determine the losses in transformer and then calculate the transformer efficiency with the help of those losses calculation. You may also read: EMF Equation Of a Transformer Transformer Efficiency, All day Efficiency & Condition for maximum Efficiency Formulas for Transformer Efficiency Efficiency = ? = Output / Input Efficiency = ?= Output / (Output + Losses) ….. (As Input = Output +Losses) Efficiency = ?= Output / (Output +Copper Losses + Iron Losses) You may also find the Efficiency by the following formula Efficiency = ?= Output / Input Efficiency = ? = (Input – Losses) / Input ….. (As Output = Input – Losses) Taking LCM Efficiency = ? = 1 – (Losses /Input) As we know that the rating of Transform is expressed in kVA not in kW. But the efficiency doesn’t depend on VA i.e. it would be expressed in Power Watts (kW) not in kVA. Although, the Losses are directly proportional to VA (Volt-Amperes), thus, efficiency depends on Power factor on every kind of VA load. And the efficiency would be maximum on unity (1) Power factor. You may also read: Power Transformers Maintenance, Diagnostic & Monitoring Good to Know We can also find transformer efficiency by determining: Core losses by open circuit test or No Load test, and Copper losses by short circuit test. Condition for Maximum Efficiency of Transformer We know that, Copper Loss = WC = I12 x R1 or I22 x R2 Iron Loss= WI = Hysteresis Loss + Eddy Current Loss = WI = WH + WE Suppose to the primary side of transformer… Primary Input = P1 = V1 x I1 Cos?1 Efficiency = ? = Output / Input Efficiency = ? = (Input – Losses) / input ….. (As Output = Input – Losses) Efficiency = ? = (Input – Copper losses – Iron Losses)/Input Efficiency = ? = (P1 – WC – WI) / P1 Efficiency = ? = (V1 x I1 Cos?1 – I12 x R1 – WI) / V1 x I1 Cos?1 Taking LCM Efficiency = ? = 1- (I12 x R1 / V1I1 Cos?1) – (WI / V1 x I1 Cos?1) Or Efficiency = ? = 1- (I1 x R1 / V1 Cos?1) – (WI / V1 x I1 Cos?1) Differentiate both sides with respect to I1 D? / dI1 = 0 – ( R1 / V1 Cos?1) + (WI /V1 x I12 Cos?1) D? / dI1= – ( R1 / V1 Cos?1) + (WI / V1 x I12 Cos?1) For Maximum Efficiency, the value of (D? / dI1) should be Minimum i.e. D? / dI1 = 0 The above Equation can be written as R1 / (V1 Cos?1) = (WI /V1 x I12 Cos?1)