Due to simplicity in construction and ease in operation and maintenance, induction motors have become the most popular prime mover, and about 80 % of the electrical drives are induction motors. An induction motor will give the best performance if the perfect sinusoidal voltage is fed to the induction motor.

V = V_{m * }sinϕ

Nowadays variable frequency drives are widely used in industrial installation because the speed control of the motor can be easily and accurately achieved with the use of VFDs.

Variable VFDs use semiconductor devices for conversion of input sinusoidal voltage to DC and again to a regulated variable voltage/ variable frequency. The inverter and converter section of VFDs have semiconductor devices like diodes and IGBTs. The semiconductor devices exhibit non-linear characteristics in applied voltage and current drawn. The nonlinearity of current with applied voltage introduces harmonics current in the electrical network. The harmonic current severely affects the performance of the induction motor.

**EFFECTS OF HARMONICS ON INDUCTION MOTORS**

The most important performance parameters of the induction motor are as follows;

**Torque-speed characteristics**

The motor should accelerate the load and continue to mechanical power as demanded by the equipment.

**Reliability**

The reliable operation of the induction motor depends on the life of the insulating material. The insulation resistance decreases as the temperature is increased. The harmonics current has a higher frequency, and because of higher frequencies of harmonics current, the eddy current and hysteresis losses increase that further leads to rising of core temperature. The shaft voltage may also be set up because of increased stray capacitance at higher-order harmonic current. The higher shaft current may fail the bearings. The bearing of the non-driving end(NDE) side of the motor must be insulated bearing or the shaft must be grounded through the carbon brush.

**TORQUE :**

The torque of the machine depends on the rotor input power.

**Rotor Input power = Stator Input power – Power losses**

Harmonic distortion causes increased losses in motors in the same way as in transformers. However additional losses arise due to the production of harmonic generated fields. Each harmonic has a sequence positive (+), negative (-), and zero (0) sequence that indicates the direction of rotation that would result if it were to be applied to an induction motor with respect to the fundamental.

Harmonic Order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

Phase Sequence | + | _ | 0 | + | _ | 0 | + | _ | 0 | + | _ | 0 |

Zero sequence harmonics (3, 6, 9, 12), the third and multiples of the third (Triplen) produce a stationary field, but since the harmonic field frequencies are higher the magnetic losses are greatly increased and the harmonic energy is dissipated as heat.

Negative sequence harmonics result in a counter-rotating field with respect to fundamentals, which results in reduced torque. Positive sequence components produce a forward rotating field that adds to the torque. The positive and negative sequence torques components result in vibration and reduce the service life of the motor.

**ANALYSIS OF INDUCTION MOTOR FED FROM NON-SINUSOIDAL VOLTAGE SUPPLY**

When supply to the induction motor is fed from an inverter or cyclo-converter, the motor terminal voltage is non-sinusoidal but it has half-wave symmetry. A non-sinusoidal waveform can be resolved into fundamental and harmonic components using Fourier analysis. Because of the **half-wave symmetry of the inverter output, only odd harmonics will be present.**

Consider the fundamental phase component V_{AN} = V_{1} sin wt, V_{BN} = V_{1} (sin wt –2∏ /3) and V_{CN} = V_{1} (sin wt –4∏ /3) with a phase sequence ABC. The corresponding 5^{th }and 7^{th} harmonic phase voltage is

V_{AN} = V_{5} sin 5wt

V_{BN} = V_{5} sin 5(wt – 2∏ /3) = V_{5} sin (5wt – 4∏ /3 )

V_{CN} = V_{5} sin 5 (wt –4∏ /3) = V_{5} sin (5wt –2∏ /3)

And

V_{AN} = V_{7} sin 7wt

V_{BN} = V_{7} sin 7(wt – 2∏ /3) = V_{5} sin (7wt – 2∏ /3 )

V_{CN} = V_{7} sin 7 (wt –4∏ /3) = V_{5} sin (7wt –4∏ /3)

The above equation shows that the 7^{th} harmonic has a phase sequence ABC, which is the same as that of the fundamental. Hence it is a positive sequence harmonic. The 5^{th} harmonic has a phase sequence ACB; hence it is a negative phase sequence harmonic. When the motor is delta connected, tripplen( harmonics ( 3,6,9……etc.)circulates in delta winding, and the harmonics current of this order does not reflect at the source side. The motor phase current will be obtained by

I^{2}_{ rms} = I^{2}_{s} + ∑ I^{2}_{m}

m=3,5…

With harmonic current, the RMS current of the motor is higher than the fundamental current. The increased current due to the presence of harmonics increases the copper loss substantially. Core loss also gets increased because of harmonic currents. Because of an increase in losses, the motor has to be de-rated in the sense that the power output that can be obtained from the machine for the same temperature rise has to be smaller. The efficiency is also reduced due to an increase in losses.

Another important effect of non-sinusoidal supply is the production of pulsating torque due to the interaction between the rotating field produced by one harmonic and the rotor current of another harmonic. Harmonics orders 5, 7, 11, 13 are major contributors to torque pulsations. 5th harmonic produces a backward rotating field, and the 7th harmonic produces a forward rotating field. As a result, the relative speed between the field produced by the fundamental and 5th and 7th harmonic current is six times the speed of fundamental. The same case is with the harmonics orders 11 and 13 that produce torque pulsation whose frequency is 12 times more than that of fundamental. When the motor supply frequency is low these torque pulsations cause pulsation in speed.

**COGGING AND CRAWLING :**

The 5^{th} and 7^{th }harmonics order current produces a resultant flux distribution in the air gap that can cause a phenomenon called cogging( Refusal to start smoothly or **crawl ( run at very high slip ).**

The synchronous speed of the motor is different for different order harmonics. When the motor starts accelerating, the base speed synchronous speed has to through the synchronous speed of harmonics. If the load torque is met with the synchronous torque produced with the 7th order harmonics, the motor speed will increase up to 1/7^{th} of the base speed. This phenomenon is known as crawling.

### **NOISE AND VIBRATION :**

The noise due to asynchronous and synchronous torques is most evident during starting. The vibratory forces are caused when the number of pairs of poles of higher harmonic fields in stator and rotor differs by 1, a magnetic pull is set up in a certain direction, and this travels around the machine, tending to make the stator-rotor oscillate. If the difference of the pole pairs is more than one, there will be several unbalance radial forces, which travel around the rotor and cause vibration and noise. The higher-order harmonics current produces the audible noise in the motor.

**EFFICIENCY & TEMPERATURE RISE :**

A major effect of harmonic voltage and current in an induction motor is increased heating due to increased iron and copper losses at the harmonic frequencies. This affects the machine efficiency and temperature rise. Due to harmonic both copper as well as iron losses increase because both the losses are frequency dependent.

### **INCREASED RESISTANCE DUE TO SKIN EFFECT :**

The current tends to flow at the outer surface of the conductor with an increased frequency. This phenomenon is known as SKIN EFFECT. The harmonic current has a higher frequency and flows at the outer surface of the conductor.

As a result, the effective area of the conductor gets reduced and the resistance of the conductor gets increased because the resistance is inversely proportional to the cross-section area of the conductor. The higher resistance leads to the higher copper loss(I ^{2}*R) in the motor.

**Related Posts**

**Harmonics and Harmonic Frequency in AC Circuits****Difference between Harmonics and Sub-Harmonics****Interharmonics in Power System****Effects of Harmonics on Transformers****Effects of Harmonics on Power Cables**

Very informative post indeed!! It helps in better understanding of the scenario occurring in induction motors!!!thanks

Informative, Concise and Understandable