Análisis Dinámico De Arranque De Motores Eléctricos

INDUCTION MOTORS: PART I - ANALYSIS
by S. E. Zocholl Schweitzer Engineering Laboratories, Inc.

INTRODUCTION
Is there ever enough information at hand to analyze a motor problem? Consider this example: A plant process is shut down for maintenance once every two years. After a scheduled maintenance, an 1800 rpm, 2.4 kV, 1200 hp pump motor tripped on startup. The plant is under new management,and few files are available. However, records list the motor starting time as 20 seconds and the locked rotor time as 14 seconds. The motor bus is fed by a transformer with a 5.6 percent impedance that dips the terminal voltage 75 percent of nominal on starting. The plant manager wants a report and a recommendation to upgrade the protection. Here is an overview of what needs to be done:

Figure1: Motor Analysis Block Diagram

Induction motor starting can be analyzed using electrical, mechanical, and thermal models which interact as diagrammed in Figure 1. In the electrical model, the voltage, V, and the slip, S, determine the rotor current. The summation of all torques acting on the motor shaft comprises the mechanical model. Here, the driving torque developed by the motor is resistedby the load torque and the moment of inertia of all the rotating elements, all of which are slip dependent. The thermal model is the equation for heat rise due to current in a conductor determined by the thermal capacity, the thermal resistance, and the slip dependent I2R watts. As the ultimate protection criteria, the thermal model is used to estimate the rotor temperature, U, resulting from thestarting condition with initial temperature U0. A recursive solution using finite time increments is used because the rotor impedance changes continuously with slip. As complex as this process may appear, we can add a few standard values and do the complete analysis with the meager information given. In fact, using the SEL-5802 Motor Modeling Program, it can be done in less than a minute. Here ishow.

1

ESTIMATING INPUT DATA
Figure 2 is the menu of the data which defines the electrical and the thermal model of the motor. To fill in the data, we have used the stated voltage and horse power to calculate the full load current:
FLA = 746 ⋅ HP 0.8 ⋅ 3 ⋅ V = 746 ⋅ 1200 0.8 ⋅ 3 ⋅ 2.400 = 269

(1)

We used 6 times FLA as the locked rotor current and calculated the full load speedusing one percent slip at full load. Depending on the class and application of the motor, the locked rotor torque can take on values of 0.8, 1.0, or 1.2. The value of 0.8 is the appropriate value for a pump motor.

Figure 2: Menu of Essential Motor Data

DEFINING THE ELECTRICAL MODEL
The program uses the motor data in the motor menu to generate the impedances of the motor including equations forthe slip dependent positive- and negative-sequence rotor resistance and reactance: Locked rotor current:
IL = LRA = 6.0 FLA

(2)

Rotor resistance at rated speed

R0 =

SynW − FLW = 0.01 SynW

(3)

2

Locked rotor resistance

R1 =

LRQ = 0.022 I2 L R0 = 0.002 5

(4)

Stator resistance

RS =

(5)

Total series resistance

R = R 1 + R S = 0.024 1 = 0.167 IL

(6)Total series impedance

Z=

(7)

Total series reactance

X = Z 2 − R 2 = 0165 . X = 0.0082 2

(8)

Locked rotor reactance

X1 =

(9)

Stator reactance

X S = X − X1 = 0.082 X 0 = (tan(12.75° ))(1+ R 0 + R S ) = 0147 . R r + = ( R1 − R 0 ) ⋅ S + R 0 X r + = ( X1 − X 0 ) ⋅ S + X 0 R r − = ( R 1 − R 0 ) ⋅ (2 − S) + R 0 X r − = ( X 1 − X 0 ) ⋅ ( 2 − S) + X 0

(10)

Rotorreactance at rated speed

(11)

Positive-sequence rotor resistance

(12)

Positive-sequence rotor reactance

(13)

Negative-sequence rotor resistance

(14)

Negative-sequence rotor reactance

(15)

The above calculations result in the equivalent circuit shown in Figure 3. We can now have the program calculate the characteristic of rotor torque and current versus slip at rated volts...