AC Circuit Phase Sequence

Phase sequence is the order in which the generated voltages in the phase winding of an alternator reach or  attain  their peak or maximum values. It is represented by the letters a, b, and c or the numbers 1, 2, 3 or by using double letter as ab, bc  and ca or  an, bn  and cn.

For instance , The three phase balanced voltages with their common magnitudes as K have sequence of a b c , then in complex form, 

Positive Phase Sequence 

ABC sequence  -  Va = Ka0˚ , Vb = a-120˚ and Vc = Ka-240˚

In this sequence Vb lags Va by 120˚ and Vc lags Vb by 120 or Vc lags Va by 240. The maximum value of Va comes first in the positive direction, next Vb and then Vc. 

ABC →BCA →CAB

AB - BC - CA → BC - CA - AB → CA - AB - BC

AN - BN - CN → BN - CN - AN → CN - AN - BN

Vector Representation

 Sequence ABC  

Sequence BCA

Sequence CAB

Negative Phase sequence 

ACB sequence- Va = Ka0˚ , Vb = a-120˚ and Vc = Ka-240˚

Voltage Vc lags Va by 120˚ and voltage Vb lags Vc by 120˚. 

ACB →CBA →BAC

AB - CA - BC → CA- BC - AB → BC - AB - BA

AN - CN - BN → CN - BN - AN → BN - AN - CN

Vector representation

Sequence BAC

Sequence  CBA

Sequence ACB

Assume a positive phase sequence if the phase sequence is not given . The three  phase alternators are designed to operate with positive phase sequence voltages.

Balanced Three phase AC circuit Delta connected

A balanced three phase AC circuit systems is energized by three equal alternating emf's of the same frequency but 120 degree apart. The phase impedance are equal. Also the currents are equal and 120 degree apart.

Three AC emf's differing in time phase by 120 degree

DELTA (MESH) CONNECTED SYSTEM
This type of connection is reffered to as 3 phase, 3 wire system. In this connection , the dissimilar ends of the 3 phase windings of a 3 phase ac generator are joined together,  for example the starting ends of one phase is joined to finishing end of the other phase so on. In other words the three winding's are joined in series to form a closed mesh. three leads are taken out from the juntions to serve as the generator terminals.

Delta connected System

Relationships: VØ = VL       :  IØ = IL/√(3)   

 Where:

        VØ  - phase voltage

        IØ  - phase current

       VL -  line voltage

       IL -  line voltage

The three phase voltages of this circuit always sum to zero  Va + Vb + Vc =0

As seen from the diaram, there is only one phase winding completely included between any pair of terminals. Hence, in delta connection, the voltage between any pair of lines is equal of the phase voltage of the phase winding connected between the two lines considered.

Electronics :Traffic light Circuit

This is a two way continuous traffic light circuit which uses  LED, diodes and IC's . 

Usually most traffic light in the world is PLC controlled but this circuit is  simple  and easy to build . 

 In the image below is the schematic diagram of the project . I used Yenka Free Software to simulate and see if its properly working . You can download it free on Yenka website.

The  clock pulses from the 555 astable circuit is sent into the 4017 decade counter . Each output becomes high in turn as the clock pulses are received. Appropriate outputs are combined with diodes to supply the amber and green LEDs. 

components :

• resistors: ,50k ohm, 10k ohm, two-100k ohm
• capacitors: 10µF 16V radial
• diodes:  16 pieces of 1N4148 
• LEDs: 2 sets of ( red, amber or yellow, green)
• IC:555 timer ,  4017 counter
•  on/off switch

You can adjust the timing of light-shifting by adjusting the  value of the resistor in the astable circuit . 

Plane Geometry Review : Triangle Area calculation

Area Formulas

1.  Given base and altitude

Triangle: Given base and height

Area = 1/2 (b)(h)

2. Given two sides and an Angle

 Triangle:  Given 2 sides and angle

Area = 1/2 (a) (b)sin θ

3. Given 3 sides

Triangle Given 3 sides a,b,c

Area = sqrt (s(s-a)(s-b)(s-c))----->  Heron's Formula  

where s= (a+b+c)/2

4. Triangle inscribed in a circle

r= radius of the circle 

Area = (a b c)/ 4r

5. Given a circle inscribed in a Triangle

r = radius of the circle

Area  =  rs 

s = ( a+b+c/) 2

6. Circle escribed by the triangle

where a is the side tangent to the circle

Area =  r (s-a)

s = ( a+b+c/) 2

Engineering Mathematics : Plane Geometry Part 1

Fundamental Principles


Angles

• Acute angle = less 90 deg
• Obtuse angle = more than 90 and less than 180 deg
• Straight angle =180 deg
• Vertex of the angle is point where two lines meet
• Supplementary angles have a sum of 180 deg
• Complementary angles have a sum of 90 deg
• The base angles of an isosceles (two equal sides) triangle =  60 deg
• Each angle of an isosceles right triangle = 45 deg
• Exterior angle of a triangle is the sum of the remote interior angle
• The sum of the angles of a polygon of n sides = (n-2)180 deg
• The sum of the exterior angles of any polygon = 360 deg

Congruence of triangle

In geometry,Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size

conditions:   (s=side  ; a=angle)

• s.a.s =s.a.s   (Side-Angle-Side)
• a.s.a=a.s.a  (Angle-Side-Angle)
• s.s.s=s.s.s  (Side-Side-Side
• a.a.s=a.a.s (Angle-Angle-Side)

Two right triangles are congruent if hypotenuse and leg of one hypotenuse and corresponding leg of the other.