## ABSTRACT

V I = R + jX amperes (8.1)

The Circle Diagram

jX

v V V I = j2X + R + jX - j2X amperes

V V[j2X - (R + jX)] 1= - +

j2X (j2X)(R + jX) amperes (8.3)

Rearranging yields

I = ~ + V(-R + jX) j2X (j2X)(R + jX)

amperes (8.4)

Multiplying the numerator and denominator by the operator j

= .::lY _ jV -R + jX = - jV + jV R - jX I 2X 2X R + jX 2X 2X R + jX amperes (8.5)

2 I = - jV + jV (R - jX)

2X 2X R2+~ - jV jV [ R - jX J 2 2X + 2X (R2 + ~?/2

amperes

(8.6)

(8.7)

144 Chapter B

where

-1( X) 8=tan -R" numeric (B. B) and where cos 8 is the power factor of the circuit in Fig. B.1. Since, from DeMoivre's theorem,

eq. (B.7) may be written as

8.3 CONCEPT OF THE CONVENTIONAL POLYPHASE INDUCTION MOTOR CIRCLE DIAGRAM

The Circle Diagram 147

Thus the no-load power factor is

-1 ° = cos n P

(VA) degrees

(8.12)

(8.13)

(8.14)

148 Chapter 8

3V1

(8.15)

(8.16)

The Circle Diagram 149

The power input to the motor, under blocked-rotor conditions, is

(8.17)

where the quantities are as defined previously, with the subscript £ denoting blocked-rotor values for those quantities that change under this condition. The total blocked-rotor volt ampere input to the motor is equal to

(8.18)

and the blocked-rotor power factor is

numeric

-1 0i = cos degrees

(8.19)

(8.20)

3V1 (8.22)

The Circle Diagram

FIGURE 8.5 Conventional circle diagram showing maximum torque, maximum power, and maximum power factor.