Renewable Energy Engineering Program
REE 311 Electric Machines
Lecture 2
Electromechanical Energy Conversion Fundamentals
Faraday’s law – Induced voltage from a time-changing magnetic field
• Faraday’s law states that if a flux passes through a coil
of wire, a voltage will be induced in the wire that is
directly proportional to the rate of change in the flux
with respect to time multiplied by the number of turns.
eind = voltage induced in coil
d
eind N N = number of turns in coil
dt Φ = flux passing through coil
• The minus sign in the equation is an expression of
Lenz’s law.
• Basis of transformer action
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Faraday’s law – Eddy current losses
• A time changing flux induces voltage within a ferromagnetic core.
• These voltages cause current to flow in loops within the core eddy currents
• These currents are flowing in a resistive material (core material) and therefore energy is
dissipated in the form of heat.
• Eddy current loss is proportional to the size of the paths they follow in the core.
Laminated cores (as thin as possible)
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Faraday’s law – Example 1-6
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Production of induced force on a wire
• A second major effect of a magnetic field is that it
induces a force on a current-carrying wire within the
field.
i = magnitude of current in wire
F i l B
l = length of wire, with direction of l defined to
be in current direction
B = magnetic flux density vector
• Direction of the force is given by the right hand rule.
F ilB sin
θ = angle between the wire and the flux density vector
• Basis of motor action
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Magnetic force – Example 1-7
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Induced voltage on a conductor moving in a magnetic field
• If a wire with the proper orientation moves through a
magnetic field, a voltage is induced in it.
v B l
v = velocity of the wire
eind l = length of conductor in the magnetic field
B = magnetic flux density vector
the
• The voltage in the wire will be built up so that
positive end is in the direction of the vector v B
• The induction of voltages in a wire moving in a
magnetic field is the fundamental to the operation of
all types of generators.
• Basis of generator action
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Magnetic force – Example 1-9
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The linear DC machine – A simple example
• A linear DC machine is the simplest machine to
understand, yet it operates with the same principle as
all other machines.
• The behavior of this machine can be explained as
follows:
1. Force induced on the wire: F i l B
2. Voltage induced on the wire moving in the field: eind v B l
3. KVL for this machine: VB eind iR
4. Newton’s law: Fnet ma
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Starting the linear DC machine
• At starting the linear DC machine behaves as follows:
1. Closing the switch produces a current flow
2. The current flow produces a force on the bar.
3. The bar accelerates to the right, producing an
induced voltage
4. This induced voltage reduces the current flow.
5. The induced force is thus decreased until eventually
F =0. At that point, the bar moves at a constant no
load speed
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Starting the linear DC machine
• At starting the linear DC machine behaves as follows:
1. Closing the switch produces a current flow
2. The current flow produces a force on the bar.
3. The bar accelerates to the right, producing an
induced voltage
4. This induced voltage reduces the current flow.
5. The induced force is thus decreased until eventually
F =0. At that point, the bar moves at a constant no
load speed
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The linear DC machine as a Motor
• When the load is connected, an induced force in the
direction of motion exists.
• Therefore power is being converted from electrical
form to mechanical form to keep the bar moving.
• The power being converted is:
Pconv eind i Find v
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The linear DC machine as a Motor
• A real dc motor behaves similarly:
1. as a load is added to the shaft, the motor begins
to slow down
2. This reduces its internal voltage
3. The current increases
4. This increases the induced torque
5. Until it is equal to the load torque
6. The motor rotates at a new speed slower than at
no load
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Thank you
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