ELL 100 INTRODUCTION TO ELECTRICAL ENGG Course Instructors

ELL 100: INTRODUCTION TO ELECTRICAL ENGG. Course Instructors: J. -B. Seo, S. Srirangarajan, S. -D. Roy, and S. Janardhanan Seo Department of Electrical Engineering, IITD

Definition of magnetic field and force – 1 Magnetic flux density (unit: tesla, T, 1 T = 1 Weber/m 2) Magnetic flux, the amount of magnetic field

Definition of magnetic field and force – 2 Magnetic flux density (unit: tesla, T, 1 T = 1 Weber/m 2) Magnetic flux, the amount of magnetic field

Definition of magnetic field and force – 2 Magnetic flux density (unit: tesla, T, 1 T = 1 Weber/m 2) Magnetic flux, the amount of magnetic field

Definition of magnetic field and force – 3 Magnetic force on a moving charge and

Definition of magnetic field and force – 4

Definition of magnetic field and force – 4

Magnetization and hysteresis Cast steel or iron Magnetic field intensity Magnetic flux density:

Magnetization and hysteresis Magnetic field intensity Magnetic flux density: residual

Magnetization and hysteresis Magnetic field intensity Magnetic flux density:

Magnetization and hysteresis Magnetic field intensity Magnetic flux density:

Lenz’s Law Magnetic force by induced current pushes the incoming magnet.

Lenz’s Law Magnetic force by induced current pushes the incoming magnet. Magnetic force by induced current pulls the outgoing magnet. Induced I always flows to oppose the movement which started it.

Current coming toward you Current going away from you

Current coming toward you Current going away from you

Current coming toward you Current going away from you

Magnetically coupled circuit Mutual inductance (positive) turns Mutual voltage (Positive or negative)

Magnetically coupled circuit Mutual inductance (positive) turns Positive or negative

Dot convention turns

Dot convention

Dot convention

Dot convention

Dot convention

Write a mesh current equation Find and F

Write a mesh current equation Find and – +

Write a mesh current equation Find and + –

Write a mesh current equation Find and – + + –

Write a mesh current equation Find and

Write a mesh current equation Find and + –

Write a mesh current equation Find and – +

Write a mesh current equation Find and + – – +

Write a mesh current equation Find and

Write a mesh current equation Find and – +

Write a mesh current equation Find and – +

Write a mesh current equation Find and – +

Write a mesh current equation Find and – +

Write a mesh current equation Find and

Write a mesh current equation Find and – +

Write a mesh current equation Find and +

Write a mesh current equation Find and +

Write a mesh current equation Find and +

Coupling coefficient and energy stored

Coupling coefficient and energy stored

Coupling coefficient and energy stored • The energy stored in the circuit cannot be negative because the circuit is passive. Coupling coefficient

Ideal transformer is one with perfect coupling and no lossless coils: and The energy supplied to the primary must equal the energy absorbed by the secondary • The ratings of transformers are usually specified as . • A transformer with rating 2400/120 V should have 2400 V on the primary and 120 in the secondary (i. e. , a step-down transformer). The voltage ratings are in rms.

Ideal transformer is one with perfect coupling and no lossless coils: and The energy supplied to the primary must equal the energy absorbed by the secondary • The ratings of transformers are usually specified as . • A transformer with rating 2400/120 V should have 2400 V on the primary and 120 in the secondary (i. e. , a step-down transformer). The voltage ratings are in rms.

Ideal transformer is one with perfect coupling and no lossless coils: and The energy supplied to the primary must equal the energy absorbed by the secondary • The ratings of transformers are usually specified as . • A transformer with rating 2400/120 V should have 2400 V on the primary and 120 in the secondary (i. e. , a step-down transformer). The voltage ratings are in rms.

Ideal transformer is one with perfect coupling and no lossless coils: and The energy supplied to the primary must equal the energy absorbed by the secondary • A transformer with rating 2400/120 V should have 2400 V on the primary and 120 in the secondary (i. e. , a step-down transformer). The voltage ratings are in rms.

Ideal transformer

Ideal transformer

Ideal transformer We are interested in finding an equivalent circuit with an ideal transformer

Ideal transformer We are interested in finding an equivalent circuit with an ideal transformer Referred to the primary

Ideal transformer We are interested in finding an equivalent circuit with an ideal transformer Referred to the secondary Referred to the primary + –

Ideal transformer We are interested in finding an equivalent circuit with an ideal transformer (due to open circuit at a and b)

Ideal transformer We are interested in finding an equivalent circuit with an ideal transformer

Ideal transformer We are interested in finding an equivalent circuit with an ideal transformer The general rule for eliminating the transformer and reflecting the secondary circuit to the primary side is (given turns ratio is n): • Divide the secondary impedance by n 2 • Divide the secondary voltage by n • Multiply the secondary current by n.

Ideal transformer We are interested in finding an equivalent circuit with an ideal transformer The general rule for eliminating the transformer and reflecting the primary circuit to the secondary side is (given turns ratio is n): • Multiply the primary impedance by n 2, • Multiply the primary voltage by n, • Divide the primary current by n.

Practical transformer •

Non ideal transformer • The ideal transformer circuit can be modified to include the non idealities. § R 1 and R 2 are due to winding resistances in the primary and secondary. § X 1 and X 2 are inductance due to leakage flux. X 0 is due to the magnetizing flux. § R 0 is due to hysteresis and eddy current losses. § Typically the series elements have very small value, and shunt elements have very large values.

Non ideal transformer

Non ideal transformer

Non ideal transformer Referred to the primary

Non ideal transformer Referred to the primary

Non ideal transformer Referred to the secondary

Non ideal transformer • In open circuit test, the low voltage side is connected to a voltage source. • The high voltage side is open circuited. Rated voltage is applied. • Voltage, current and power are measured. V • A 20 k. VA 2500/250 V, 50 Hz single phase transformer gave the following test result: Open circuit test on low voltage (LV) side: 250 V, 1. 4 A, 105 W

Non ideal transformer • In open circuit test, the low voltage side is connected to a voltage source. • The high voltage side is open circuited. Rated voltage is applied. • Voltage, current and power are measured. V • This test estimates iron or core loss in a transformer • A transformer with 20 k. VA 2500/250 V, 50 Hz single phase transformer gave the magnetizing current VA rating following test result: § Open circuit test on low voltage (LV) side: 250 V, 1. 4 A, 105 W measurements

Non ideal transformer Core (iron) loss • A 20 k. VA 2500/250 V, 50 Hz single phase transformer § Open circuit test on low voltage (LV) side: 250 V, 1. 4 A, 105 W Power factor V (Full voltage on LV)

Non ideal transformer • A 20 k. VA 2500/250 V, 50 Hz single phase transformer § Open circuit test on low voltage (LV) side: 250 V, 1. 4 A, 105 W V

Non ideal transformer • A 20 k. VA 2500/250 V, 50 Hz single phase transformer § Open circuit test on low voltage (LV) side: 250 V, 1. 4 A, 105 W V

Non ideal transformer • In short circuit test, the low voltage side is short circuited. • Apply the voltage on the high voltage side to flow the rated current flow • Voltage, current and power are measured. (referred to the primary) Note that • We assume . and • This test estimates copper loss. and .

Non ideal transformer • The low voltage side of the transformer is shorted and voltage is applied to the high voltage side, because it only takes about 4%-7% of rated voltage to cause rated current to flow in the winding. • Transformer with 20 k. VA, 2500/250 V:

Non ideal transformer Copper loss • Short circuit test on high voltage side: 8 A, 104 V, 320 W and

Non ideal transformer • Short circuit test on high voltage side: 8 A, 104 V, 320 W and (Reduced high voltage)

Non ideal transformer • Short circuit test on high voltage side: 8 A, 104 V, 320 W and

Example • 2000 -VA, 230/115 V transformer has been tested to determine its equivalent circuit. The following measurements are taken the primary side of the transformer, i. e. , HV. 1) Estimate the parameters. 2) Find the equivalent circuit referred to the secondary (or LV side) • Open circuit test: Voc = 230 V, Ioc=0. 45 A, Woc=30 • Short circuit test: Vsc = 13. 2 V, Isc=6 A, Wsc=20. 1 Solution By using the measurements with open-circuit test, we get

Example • 2000 -VA, 230/115 V transformer has been tested to determine its equivalent circuit. The following measurements are taken the primary side of the transformer, i. e. , HV. Estimate the parameters. 2) Find the equivalent circuit referred to the secondary (or LV side) • Open circuit test: Voc = 230 V, Ioc=0. 45 A, Woc=30 • Short circuit test: Vsc = 13. 2 V, Isc=6 A, Wsc=20. 1 Solution By using the measurements with short-circuit test, we get

Example • Now, to find the equivalent circuit referred to the secondary, we use the following: and From and

Non ideal transformer • Efficiency,

Ideal transformer • The complex power in the primary winding is (in rms value) • Input impedance for the circuit with an ideal transformer: • This input impedance is called the reflected impedance, since it appears as if the load impedance is reflected to the primary side

Ideal transformer • The complex power in the primary winding is (in rms value) • Input impedance for the circuit with an ideal transformer: • This input impedance is called the reflected impedance, since it appears as if the load impedance is reflected to the primary side

Example • Find: (a) the source current , (b) the output voltage , and (c) the complex power supplied by the source.