Electrical Drives

1. ELECTRICAL DRIVES & INSTRUMENTATION
EEE-105
Lecture -2

2. CHAPTER-1
FARADAY'S LAW- Induced Voltage from a Time-Changing
Magnetic Field:
 Faraday's law states that if a flux passes through a turn of a
coil of wire, a voltage will be induced in the turn of wire that
is directly proportional to the rate of change in the flux with
respect to time.
 If a coil has N turns and if the same flux passes through all
of them, then the voltage induced across the whole coil is
given by,

3. CHAPTER-1
The minus sign in the equations is an expression of Lenz’s law.
 Lenz's law states that the direction of the voltage buildup in the
coil is such that if the coil ends were short circuited, it would
produce current that would cause a flux opposing the original flux
change.

4. TRANSFORMERS_(CHAPTER-2)
Main Parts of a TRANSFORMER:

5. TRANSFORMERS_(CHAPTER-2)
Construction of TRANSFORMERS:
 Power transformers are constructed on one of two types
of cores. One type of construction consists of a simple
rectangular laminated piece of steel with the transformer
windings wrapped around two sides of the rectangle. This
type of construction is known as core form.

6. CONSTRUCTION OF TRANSFORMERS:
 The other type consists of a three-legged laminated
core with the windings wrapped around the center leg.
This type of construction is known as shell form.

7. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 An ideal transformer is a lossless device with an input winding
and an output winding.
 The transformer shown in Figure
Np - Turns of wire on its primary side.
Ns - Turns of wire on its secondary side.
 The turns ratio (a) of the transformer:

8. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 𝑣𝑝(t) – The applied voltage to the primary side of the transformer.
 𝑣𝑠(t) – The produced voltage on the secondary side of the
transformer.
So, The relation -------
 𝑖𝑝(t) - The current flowing into the primary side of the
transformer.
 𝑖𝑠(t) - The current flowing out of the secondary side of the
transformer.
So, The relation -------

9. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 Finally,
 Notice that the phase angle of Vp is the same as the angle of Vs
and the phase angle of Ip is the same as the phase angle of Is.
The turns ratio of the ideal transformer affects the magnitudes
of the voltages and currents, but not their angles.

10. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 Dot Convention:
The dots appearing at one end of each winding to tell the polarity of the
voltage and current on the secondary side of the transformer. The
relationship is as follows:
1. If the primary voltage is positive at the dotted end of the winding
with respect to the undotted end, then the secondary voltage will be
positive at the dotted end also. Voltage polarities are the same with
respect to the dots on each side of the core.
2. If the primary current of the transformer flows into the dotted end
of the primary winding, the secondary current will flow out of the
dotted end of the secondary winding.

11. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
Power in an Ideal Transformer:
 The power supplied to the transformer by the primary circuit is
given by the equation,
where 𝜽𝑷is the angle between 𝑉𝑃 and 𝐼𝑃.
 The power supplied by the transformer secondary circuit to its
loads is given by the equation,
where 𝜽𝑺 is the angle between 𝑉𝑆 and 𝐼𝑆.

12. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
Power in an Ideal Transformer:
 Applying the turns-ratio equations gives Vs = Vp/a and Is = alp.
So,
 Thus, the output power of an ideal transformer is equal to its input
power.
 The same relationship applies to reactive power Q and
apparent power S:

13. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 Impedance Transformation through a Transformer
The impedance of a device or an element is defined as the ratio of
the phasor voltage across it to the phasor current flowing through it:

14. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 Impedance Transformation through a Transformer
 One of the interesting properties of a transformer is that, since it
changes voltage and current levels, it changes the ratio between
voltage and current and hence the apparent impedance of an
element.
 If, the secondary current is Is and the secondary voltage Vs, then
the impedance of the load is given by,

15. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 Impedance Transformation through a Transformer:
 The apparent impedance of the primary circuit of the transformer
is,
 Since the primary voltage can be expressed as Vp = aVs and the
primary current can be expressed as Ip =
𝐼𝑆
𝑎

16. TRANSFORMERS_ (CHAPTER-2)
THE IDEAL TRANSFORMER
 Impedance Transformation through a Transformer:
 The apparent impedance of the primary is,
 With a transformer, it is possible to match the magnitude of a
load impedance to a source impedance simply by picking the
proper turns ratio.