How to Draw Circle Diagram of Induction Motor in Matlab

The Circle Diagram of an Induction motor is very useful to study its performance under all operating conditions. The structure of the circumvolve diagram is based on the guess equivalent circuit shown beneath. Information technology is the diagrammatic representation of the performance of the induction motor. The circle diagram provides data nigh the ability output, losses, and the efficiency of the induction motor.

Contents:

• Construction of the Circle Diagram
• Result Obtained from the Circle Diagram
• Significance of lines on the Circumvolve Diagram

Applying KCL (Kirchhoff's Current Law)

Let the phase voltage 5_i exist taken along the vertical centrality OY as shown in the figure beneath:

The No-Load current I₀ = OA lags behind 5₁ by an angle ϕ₀. The no-load ability gene bending ϕ₀ is of the club of 60 to 80 degrees considering of the big magnetizing current needed to produce the required flux pole in a magnetic circuit containing the air gaps.

At the no-load condition, due south = 0 and R₂/south are infinite, or we tin say that the R₂/s is an open up circuit at no load.

Here, all the rotational losses are considered nether R₀ and the no-load loss is given by the equation shown below:

The rotor current referred to the stator is given by:

The current I'₂ lags behind the voltage V₁ past the impedance bending ϕ every bit shown in the effigy below:

Where,

Combining equation (1) and (2) we get

The above equation (3) is of the form r = a sin φ which represents a circumvolve in polar course with the bore a.

From the in a higher place figure (b) shown, the following points are illustrated.

• The locus of I'_two is a circle of the diameter V₁/ X₁ + X'₂
• The radius of the circumvolve O'C = Five₁/ 2(X_one + X'₂)
• The centre C has the coordinates [V₁/ two(10₁ + 10'₂), 0]

The resulting circle diagram of the induction motor is shown below:

It is seen that the tip of the phasor I₁ coincides with that of the phasor I'₂. Thus, the locus of both I_ane and I'₂ is the upper semicircle. I₁ and I'₂ radiate from the origin O and O' respectively. When the motor is started s = one with the rated voltage, the tip of I₁ and I'_two will be at some point F of the circumvolve.

As the motor accelerates, the tips of I_i and I'₂ move effectually the circle in an anti-clockwise direction. This process continues until the output torque matches the load torque. If there is no shaft load, the motor accelerates to synchronous speed. At this betoken I'₂ = 0 and I₁ = 0.

Construction of the Circumvolve Diagram

The following data are required for amalgam the circle diagram:

• Stator stage voltage Five₁ = V_L/√3
• No-load current I₀
• No-load power cistron cosϕ₀
• Blocked rotor current and power factor
• Stator phase resistance R₁.

Steps to describe Circle Diagram of an Induction Motor:

• Take the phasor voltage V_i along the y-axis.
• Choose a user-friendly current. With O every bit origin, draw a line OO' = I₀ at an angle ϕ₀ with V_one.
• Draw the line OKN perpendicular to Five_one. Similarly, depict a line O'D perpendicular to V_i.
• From signal O depict the line equal to the blocked rotor current I_1BR to the same scale as I₀. This line lags behind V_i by the blocked rotor power factor angle ϕ_1BR.
• Bring together O'F and measure its magnitude in amperes. The line O'F represents I'_2BR.
• From point F, draw a line FMN parallel to 5_i. This line is perpendicular to O'D and ON.
• Calculate MS = I'² _2BRR₁/V_ane and locate signal S. Bring together O'S and extends it to meet the circle at J.
• Describe the perpendicular bisector of the chord O'F. This bisector will pass through the middle of the circle at betoken C. Now with the radius CD' or CD draw the circle.

Issue Obtained from the Circle Diagram

Assume that the line current I_ane is known. With the centre at O, draw an arc with the radius I_ane. This arc intersects the circle at the operating betoken E. Draw the line EK and locates the betoken H, L, G.

The following results are obtained from the circumvolve diagram shown above.

• Input ability = 3V₁ KE
• Rotational losses = 3V₁ KH
• Stator copper loss = 3V_ane HL
• Rotor copper loss = 3V₁ LG
• Output power = 3V_i GE
• Output torque = 3V₁ LE/ω_{due south}
• Starting torque = 3V_ane SF/ω_s
• Slip = LG/LE
• Speed = GE/LE Ten n_s
• Efficiency = GE/KE
• Power gene = KE/OE

Significance of lines on the Circle Diagram

Input line ON

The vertical distance between any point on the circle and the line ON represents the input power. Therefore, line ON is called the input line.

Output Line O'F

The vertical distance between any betoken on the circumvolve and the line O'G represents the output power. Hence, line O'F is called the output line.

Air Gap Power Line O'J

Line EL represents the air gap power P_g; line O'L is referred to as the air gap power line. Since, Ʈ_d = P_g/ ω_s. This line is also known as Torque line.

couchjoiny1968.blogspot.com

Source: https://circuitglobe.com/circle-diagram-of-an-induction-motor.html

Share this post