Equivalent Circuit of Transformer By : Dr. Atul R. Phadke Associate Professor in Electrical Engineering Government College of Engineering, Karad (Maharashtra) EQUIVALENT CIRCUIT OF TRANSFORMER: I1 V1 π 1 π1 Ideal Transformer E1 E2 N1 π 2 π2 I2 V2 ZL N2 It is possible to construct an equivalent circuit of transformer by adding the effect of imperfections to an ideal transformer. Practical transformers have winding resistances. Their effect can be considered by connecting resistances π 1 and π 2 in series with the primary and secondary windings respectively. Similarly, to include the effect of magnetic leakage, leakage reactances π1 and π2 are connected in series with the primary and secondary windings respectively. Load is represented by impedance ππΏ . When it is connected across secondary, current πΌ2 flows in the secondary circuit. 2 EQUIVALENT CIRCUIT OF TRANSFORMER: πΌ1 = πΌ0I1+ πΌ2′ π 1 π1 Iw V1 π 0 Ideal Transformer πΌ2′ I0 π0 π 2 π2 I2 Iµ E1 E2 N1 V2 ZL N2 When secondary is loaded, load component of primary current πΌ2′ flows in primary. Now the primary current is πΌ1 = πΌ0 + πΌ2′ The no load current πΌ0 is the phasor sum of the magnetizing component πΌπ and the working component πΌπ€ . Magnetizing component πΌπ is lagging behind the voltage by 900. So, its path can be represented by pure inductance X0. Working component πΌπ€ is in phase with voltage. So, its path can be represented by a non-inductive resistance R0. Current πΌ0 can be simulated by parallel combination of R0 and X0 connected across the primary circuit. 3 POINTS TO REMEMBER: When resistance, reactance or impedance is transferred from secondary to primary, it is divided by πΎ 2 . When resistance, reactance or impedance is transferred from primary to secondary, it is multiplied by πΎ 2 . When current is transferred from secondary to primary, it is multiplied by K. When current is transferred from primary to secondary, it is divided by K. When voltage is transferred from secondary to primary, it is divided by K. When voltage is transferred from primary to secondary, it is multiplied by K. 4 EQUIVALENT CIRCUIT OF TRANSFORMER REFERRED TO PRIMARY: I1 π 1 π1 Iw π 0 V1 πΌ2′ I0 Ideal Transformer π 1 π0 E1 π1 Iw V1 π 0 π0 I2 V2 E2 ZL N2 π 2′ = I0 π2 Iµ N1 I1 π 2 π 2ΰ΅ π2ΰ΅ ′ π = 2 π πΎ π 2 2 2 πΎ 2 πΌ2II′22 = πΌ2 πΎ Iµ πΈ22′ = E1 = E πΈ2ΰ΅ πΎ π2′ = π π2ΰ΅ ′ V2πΎ ZπLπΏ = πΏΰ΅πΎ 2 5 SIMPLIFIED EQUIVALENT CIRCUIT OF TRANSFORMER REFERRED TO PRIMARY: π 1 I1 π 2′ = π1 I0 Iw π 0 V1 Iµ π0 πΈ22′ = E1 = E π 01 = π 1 + π 2′ πΌ2′ I1 Iw V1 π 0 I0 π0 π 1 π 2′ = π 2ΰ΅ π2ΰ΅ ′ π = 2 π πΎ π 2 2 2 πΎ 2 πΌ2II′22 = πΌ2 πΎ π 2ΰ΅ πΎ2 πΈ2ΰ΅ πΎ π2′ = π π2ΰ΅ ′ V2πΎ ZπLπΏ = πΏΰ΅πΎ 2 π01 = π1 + π2′ π1 π2′ = π2ΰ΅ πΎ2 Iµ π2′V2 ππΏ ′ ZπLπΏ = ΰ΅πΎ 2 6 APPROXIMATE EQUIVALENT CIRCUIT OF TRANSFORMER REFERRED TO PRIMARY: π 01 = π 1 + π 2′ πΌ2′ I1 Iw V1 π 0 I0 π 1 π 2′ = π 2ΰ΅ πΎ2 π01 = π1 + π2′ π1 π2′ = π2ΰ΅ πΎ2 Iµ π2′V2 π0 πΌ1 = πΌ2′ π 01 V1 π ZπLπΏ′ = πΏΰ΅ 2 πΎ π01 π2′ ππΏ′ 7 SIMPLIFIED EQUIVALENT CIRCUIT OF TRANSFORMER REFERRED TO SECONDARY: π 02 = π 2 + π 1′ πΌ πΌ1′ = 1ΰ΅πΎ πΌπ€ΰ΅ πΎ E2 π02 = π1 + π2′ π 1′ = π 1 πΎ 2 π 2 πΌ πΌ0′ = 0ΰ΅πΎ πΌπ ΰ΅ πΎ π2 π1′ = π1 πΎ 2 πΌ2 V2 V2 π0′ = π0 πΎ 2 π 0′ = π 0 πΎ 2 πΌ2 I2 π 02 π02 ππΏ I2 π02 E2 V2 V2 ππΏ 8
