Effect Analysis of Voltage Fluctuation on Electromotor

 

Introduction

All of Shini five series products adopt three-phase asynchronous motors, particularly high power ones of large scale granulators, which drive a heavy load and have a high requirement for parameters like voltage quality and startup torque. Due to a lot of reasons supply voltage may be non-constant with up and down. This article is to analyze what effects of voltage fluctuation will bring about to three-phase asynchronous motors.

 

Supply voltage decreases

1 Effects on torque T and rotating speed n

Formula of electromagnetic torque:

 

 

For normal squirrel-cage motor, slip speed S is substantially less than 1 within stable working range. Thus SX₂₀ is substantially less than R2. Formula 1 approximates:

 

 

In this formula,   is the Constant.

 

Formula 2 indicates that when supply voltage drops, magnetic torque T will decrease directly as U_^2. When supply voltage drops by the value of a, slip speed needs to increase by times of a_² so that motor may keep a balance between original magnetic torque and load torque. The process can be illustrated by the curve of mechanical characteristic as followed:

 

 

Picture 1 Mechanical Characteristic of Asynchronous Motor

 

Curve 1 stands for the mechanical characteristic when voltage is U₁. A is the cross point with constant load torque T_f, and corresponding S is slip speed value during stable operation. If voltage falls suddenly to U₁(U₁＝U₁/a), the relevant characteristic is curve 2. During the moment of voltage dropdown, inertia makes it too late for motor change the rotating speed. Thus its magnetic torque is T corresponded to B. Because T is smaller than T_f, motor begins to slow and S value increases. As slip speed S increases, magnetic torque rises again to point C. Then magnetic torque is equal to load torque, that is T=T_f. At this time, motor drives the load to run with lower rotating speed, which drops from n=(1-S)nS to n=(1-S)nS.

 

If pressure U falls greatly, it will render peak torque smaller than load torque. In that case, motor will stop running due to failure to drive the load. And the current of rotor and stator exceeds rated value greatly, thus if no power cut-off in short time, motor will be burn down.

 

2 Effects on the current of rotor winding and stator winding

The formula of rotor current in three-phase asynchronous motor is:

 

 

In the formula, when E₂₀ is equal to S1, electromotive force of rotor each phase varies directly as stator pressure U₁.

If E₂₀＝βU₁, when motor is under normal operation SX₂₀ is substantially less than R₂. Thus expression of I₂ can be concluded as below:

 

 

In formula,  is the Constant.

When voltage U₁ falls by value of a, S should be increased by times of a₂ to keep output torque constant. Thus rotor current is:

 

 

 

It shows that current by phase of rotor increase by times of a. Because current relation between stator and rotor winding in three-phase asynchronous motor resembles that of primary and secondary winding in transformer, increasing of rotor current will certainly make current of stator winding increase, which cause motor overheat. Whats worse, if things go on like this, motor service life will be shortened and burn up.

 

When motor goes non-load running, rotor rotating speed is close to that of rotating magnetic field. Relative speed between them is very low and rotor current is almost 0, at that moment, stator current is nearly the same as exciting current that builds rotating magnetic field.

 

3 Effects on starting current I_q

In the instant of startup, n=0 and S=1, there is a big relative speed in rotating magnetic field for stationary rotor. The cutting speed of magnetic line of force on rotor conductor is very fast and the electromotive force sensed by rotor and rotor current are very large. If supply voltage decreases, the relative speed in magnetic field does not drop down and equivalent impedance of motor remains constant. Therefore, when supply voltage falls, startup current will falls.

 

4 Effects on power factor cosφ

Due to the decline of U₁, main flux in stator winding will be weakened, which makes induced electromotive force E produced by main flux in each stator phase winding drop down. Thus based on formula (6),

 

 

 

Because output torque remain constant, I₁ will increase as U₁ decreases, thus value of  will be reduced. According to formula (7),

 

 

 

Value of cosφ will increase (R₁ is resistance of stator each phase winding, it is constant value).

 

5 Effects on efficiency η

It is necessary to analyze this kind of effect from two aspects, one is full load and another is half load. Based on the formula,

 

 

 

In the formula,
P_ω and Pω2 stands for copper loss of stator and rotor winding;
P_m stands for total mechanical loss;
P_θ stands for added loss.
It can be concluded when full load that: 

 

 

 

In the formula, I₁ and I₂ stand for the current of stator and rotor winding respectively after supply voltage drops down.

Because I₁ and I₂ would increase after supply voltage decreases, so η₁<η. When it is half load:

 

 

Because P₂ is substantially larger than P_Fe, and it is impossible for stator and rotor current to increase by times of √2, η₂ should be larger than η.

To sum up, when supply voltage decreases, rotating speed, torque, startup current and efficiency in full load of three-phase asynchronous motor will be reduced. At the same time, the current of rotor and stator winding, power factor and efficiency in half load will increase.

 

Supply voltage increases

When voltage increases, parameters of three-phase asynchronous motor would be changed adversely compared to the situation of voltage decreasing. According to the formula of stator circuit,

 

 

 

It is concluded that main flux φ will increase as directly voltage U₁. Due to the nonlinearity of excitation, exciting current component will increase rapidly, which makes stator total current increase and iron-core loss increase as well, leading to overheat of motor winding and even burn up.

 

Based on above results, the fluctuation of supply voltage may influence the performance of three-phase asynchronous motor greatly. Therefore, the acceptable fluctuation range of motor voltage should be range of nominal tension between 95%~105% so that motor can output rated power.