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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 02 Issue: 01 | Apr-2015 www.irjet.net p-ISSN: 2395-0072
© 2015, IRJET.NET- All Rights Reserved Page 162
Management of power factor and harmonic
P. K. Kurundwade1, G. V. Swami 2, R. A. Metri3, S. B. Patil4, P. B. Patil5, M. Patil6
1 2 4 5 6Student, B. Tech. Electrical, Rajarambapu Institute of technology, Maharashtra, India.
3 Assistant Professor, Electrical, Rajarambapu Institute of technology, Maharashtra, India.
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - This paper discusses about the power factor
improvement and reduction in harmonic system. Poor
power factor causes increased electricity charges, penalty
for low power factor and unnecessary effect in the system
and poor power quality. To smooth such negative effects, the
power factor correction is carried out, also reduce harmonic
content in the system filters are used. Automatic Power
Factor Correction relay is one of the smart relay used to
control the capacitor with respect to output. The proposed
system is characterized by no generation of harmonics and
reduction of transmission losses.
Key Words: Harmonics, Power Quality, Power factor
correction.
1. INTRODUCTION
In power system, power factor and harmonics plays
very important role. For optimum utilization of available
power the reactive power consumption should be reduced
or nullified i.e. power factor should be unity.
As we know the most of industrial load is inductive
which causes the production of low power factor and
harmonics respectively. Power factor correction (PFC) is a
technique of counteracting the undesirable effects of
electric loads that create a power factor that is less than
one. Power factor correction maybe applied either by an
electrical power transmission utility to improve the
stability and efficiency of the transmission network or
correction may be installed by individual electrical
customers to reduce the costs charged to them by their
electricity supplier. For stable load the fixed KVAR
compensation is required, while for variable load the KVAR
requirement also changes as per the load duration cycle,
thus in such cases the automatic power factor control panel
is required.
1.1 POWER FACTOR
In general power factor is the capacity of the equipment
to do the work. In electrical field, it is another form of
energy which is transferred in per unit time. In AC circuits
we have inductor and capacitor as components. Inductor
stores energy in magnetic energy form where as capacitor
stores in electrostatic energy form. None of them dissipates
it.
Further there is phase shift of 900 between voltage and
current, but the circuit containing resistor (R), inductor (L),
capacitor (C) has some phase difference angle between
voltage and current. And the cosine of this angle (angle
between voltage and current) is known as power factor.
The value of the power factor will be always between 0 to,
which represents the fraction of total power that is used to
do the useful work.
Causes of low power factor
i. Single phase and three phase induction motor
ii. Varying load in power system
iii. Industrial heating furnaces
iv. Electrical discharge lamps, Arc lamps
v. Transformers
vi. Harmonic currents
Effect of low power factor
i. Increase in losses
ii. Large KVA rating, size of electrical equipment
iii. Greater conductor size and cost
iv. Poor voltage regulation and large voltage drop
v. Penalty from electric power supply company on
low power factor
Methods for improvement of power factor
i. Static capacitor bank
ii. Synchronous condenser
iii. Phase advancer
The most commonly used method for power factor
improvement is the static capacitor bank.
1.2 HARMONICS
It is a component of a periodic wave having a frequency
that is an integral multiple of the fundamental power line
frequency. Due to contribution of all harmonics present in
the system distribution of wave occurs and total harmonic
distortion can be calculated.
There are two types of harmonics one is characteristic
harmonics and other is non-characteristic harmonics.
1. Characteristic harmonics
It is a signal or wave having integral multiple of
frequency of the fundamental signal or wave. It
can be calculated by following equation
H = (n × p) ± 1
2. Non-characteristic harmonics
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 02 Issue: 01 | Jan-2015 www.irjet.net p-ISSN: 2395-0072
© 2015, IRJET.NET- All Rights Reserved Page 163
It is a signal or wave having other than
characteristic harmonics which are not integral
multiple of fundamental frequency is known as
non-characteristic harmonics.
Causes of harmonics
i. Use of power electronic devices
ii. Variable frequency drives
iii. Linear and non-linear loads
Effects of harmonics
Harmonics present in the system will affect the
following things
i. Conductor overheating
ii. Capacitors
iii. Fuses and circuit breakers
iv. Transformer
v. Generators
vi. Utility meters
vii. Drives or power supplies
viii. Computer and telephones
Methods for suppressing harmonics
i. No load
ii. DC choke
iii. Line reactor
iv. 12-pulse converter
v. 12-pulse distribution
vi. Harmonic trap filter
vii. Broadband filters
Mostly filter are used for harmonics reduction.
1.3 CALCULATION OF CAPACITOR VALUE
Calculation of power factor from current and required
power value.
Active current Im =current value *actual power factor
Active current I=I*required power factor
I=Im/required power factor
Reactive current Im=Current value*sinǾa
Reactive current I=I*sinǾr
Ic=Reactive component of current Im – Reactive
component current I
Ic=V/Xc
1/Xc=2*Π*f*c
Ic=V*2* Π*f*c
2. APFC RELAY
For optimum utilization of available power the reactive
power consumption should be reduced means power
factor should be unity , hence, most of the Power
Distribution companies have policy to penalize the
industrial and commercial consumers for not maintaining
power factor above certain limit i.e. above 0.90 value.
1. Need for Automatic Power Factor Correction
Normally there is varying power demand on the supply
system. Therefore power factor also varies as a function of
the load requirements and it is difficult to maintain a
consistent power factor by use of fixed compensation i.e.
fixed capacitors. When there is leading power factor under
light load conditions (fixed compensation) results in over
voltages, saturation of transformers and so the industry
penalties by electric supply authorities.
Where in APFC due to automatically variation, without
manual intervention, the compensation to suit the load
requirements, leading power factor will be also prevented.
However, due to reactive power drawn by capacitive or
inductive load in the consumer premises the power factor
is either lagging or leading, thus to maintain it within limit
i.e. for compensating or supplying required KVAR, the
capacitors or reactors in case lagging or leading PF are
connected across the system. Therefore for the variable
load the APFC panel is installed.
The major components of APFC panel comprises of
capacitor or inductor segregated in various stages, Power
Factor control Relay and contactors (ON/OFF). The APFC
relay monitors the various electrical parameters such as
KVAR requirement, Power factor, Voltage, Current and
Power consumption, of the system and uses its intelligence
to control the parameters within required limit. Thus by
sensing actual voltage and current of the system the APFC
relay computes the system power factor and KVAR
requirement, and by the control signal relay
connects/disconnects the capacitor bank to the system
with the help of contactors.
2.1 HARMONIC FILTER
Capacitor bank connected with an inductor in order to
reduce the harmonic effects. This combination constitutes
a filter for harmonics.
Previously, to avoid the negative effects of resonance,
we have to insert an inductor in series with capacitor. But
it is possible to think of placing in a point of the
combination of an inductor and capacitor well
dimensioned in order to get same resonance frequency for
eliminating the harmonic current
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 02 Issue: 01 | Jan-2015 www.irjet.net p-ISSN: 2395-0072
© 2015, IRJET.NET- All Rights Reserved Page 164
In this way combination of inductor-capacitor presents
a very low reactance in order to harmonics eliminated
which shall circulate in the assembly without affecting the
whole network. This filter is called as “passive filter”. They
are defined on a case basis, according to particular
harmonic is filtered and they are cost effective and easy to
be connected into the function.
“Active filter” are instead automatically eliminate the
current harmonics present in the network in wide range of
frequency. They can inject a system of harmonics which is
able to which neutralize those present in the network. The
active filter has an advantage that filtering simultaneously
dozens of harmonics as well as it does not involve design
cost for dimensioning.
A. CAPACITOR BANK
Capacitors are used to cancel the lagging current effects.
Capacitor also can reduce system losses as well as help to
provide voltage support. Another one benefit of capacitor is
they can reduce the total current flowing through a wire,
therefore leaving capacity in the conductors for additional
load.
Capacitor banks can be switched manually,
automatically locally. For example, system control centers
operator switch capacitor bank on and off to meet load
requirements or system stability reactive power demand
requirements. By using capacitive support we can maintain
the good system voltage and reduce the system losses as
well as maintain the power factor.
B. CONTACTORS
A contactor is a electrically controlled switch, and it is
used for switching a power circuit. A contactor is a very
heavy duty so relay used for switching magnitude. Alloy
containing silver is used for high current contacts. The
unavoidable arcing causes the contacts to oxidize and
silver oxide is still a good conductor. The overload sensing
devices are a form of heat operated relay where a coil heats
a bi-metal strip, or where a solder pot melts, releasing a
spring to operate auxiliary contacts. These auxiliary
contacts are in series with the coil. If the overload senses
excess current in the load, the coil is de-energized.
Contactor relays can be extremely loud to operate, making
them unfit for use where noise is a chief concern.
UA contactors are used for the switching of capacitor
banks. For capacitor banks inrush current do not exceed
100 times the rated current. The capacitors must be
discharged. And in this case their electrical life
corresponds to 100,000 operations. A and AF contactors
are also suited for capacitor bank switching with peak
currents lower than 30 times the rated current.
C. MCB
A circuit breaker is an automatically operated
electrical switch. It used to protect an electrical circuit from
damage caused by overload or short circuit. Its basic
function is to detect fault condition and, by interrupting
continuity, to immediately discontinue electrical flow.
Unlike a fuse, which operates once and then must be
replaced, a circuit breaker can be reset to resume normal
operation.
3. CONCLUSIONS
The proposed single-phase and three-phase automatic
power factor correction system has certain reactive
current or reactive power ratings. The proposed system
performs better than the traditional methods in mitigating
harmonics and power factor improvement.
REFERENCES
[1] A. R. Shete, A. R. Thorat, “The case study of automatic
power factor controller on distorted system with
overview of harmonics reduction technique.”
[2] IEEE Guide for application of shunt power capacitors,
IEEE Std. 1036-1992, 1992.
[3] T. A. Short, Electric power distribution handbook,
second edition, CRC press.
[4] Jain Sandesh, Thakur Shivendra Singh and
Phulambrikar S.P., “Improvent power factor and
Reduce Harmonics Distortion of the system”,
Research Journal of Engineering Sciences, November
2012.
[5] V. K. Mehta, Rohit Mehta, “Principle of power system”,
Revised edition, 2008.
[6] Miller T. J. “Reactive power control in Electric
System”, John Willey & Sons
[7] Roger C. Dugan, Mark F. Mcgranaghan, surya Santos
and H. Wayne Beaty, “Electrical power system
Quality”, Tata McGraw Hills publications
[8] Sreenivasa reddy mulla , “Power Factor Correction”,
IJIES, ISSN:2319-9598, vol. 1,Issue:- 12 November
2013.
[9] Mr. A. K. Tiwari, Mrs. D. Sharma, Mr. V. K. Sharma.
“Automatic power factor correction using capacitive
bank”, IJERA, ISSN: 2248-9622, vol. 4, issue 2
(version 1), February 2014, pp. 393-395.
[10] www.wikipedia.com
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 02 Issue: 01 | Jan-2015 www.irjet.net p-ISSN: 2395-0072
© 2015, IRJET.NET- All Rights Reserved Page 165
BIOGRAPHIES
Pratiksha K. Kurundwade is a
student B.Tech in Electrical
engineering department,
Rajarambapu Institute of
Technology, Sakharale,
Rajaramnagar, Maharashtra,
India.
Geetanjali V. Swami is a student
B.Tech in Electrical engineering
department, Rajarambapu
Institute of Technology,
Sakharale, Rajaramnagar,
Maharashtra, India.
Rajanikant A. Metri is Assistant
Professor in Electrical
engineering department,
Rajarambapu Institute of
Technology,Sakharale,
Rajaramnagar, Maharashtra,
India. He has completed his post-
graduation from College of
Engineering, Pune (CoEP). He has
4 years of teaching experience
and one year of industry
experience. He has 05
publications in various National
and International Conference and
Journals. His research area is
non-linear control and sliding
mode control.
Snehal B. Patil is a student B.Tech
in Electrical engineering
department, Rajarambapu
Institute of Technology,
Sakharale, Rajaramnagar,
Maharashtra, India.
Pallavi B. Patil is a student B.Tech
in Electrical engineering
department, Rajarambapu
Institute of Technology,
Sakharale, Rajaramnagar,
Maharashtra, India.
Madhuri . Patil is a student B.Tech
in Electrical engineering
department, Rajarambapu
Institute of Technology,
Sakharale, Rajaramnagar,
Maharashtra, India.

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IRJET-Management of power factor and harmonic

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 02 Issue: 01 | Apr-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET.NET- All Rights Reserved Page 162 Management of power factor and harmonic P. K. Kurundwade1, G. V. Swami 2, R. A. Metri3, S. B. Patil4, P. B. Patil5, M. Patil6 1 2 4 5 6Student, B. Tech. Electrical, Rajarambapu Institute of technology, Maharashtra, India. 3 Assistant Professor, Electrical, Rajarambapu Institute of technology, Maharashtra, India. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - This paper discusses about the power factor improvement and reduction in harmonic system. Poor power factor causes increased electricity charges, penalty for low power factor and unnecessary effect in the system and poor power quality. To smooth such negative effects, the power factor correction is carried out, also reduce harmonic content in the system filters are used. Automatic Power Factor Correction relay is one of the smart relay used to control the capacitor with respect to output. The proposed system is characterized by no generation of harmonics and reduction of transmission losses. Key Words: Harmonics, Power Quality, Power factor correction. 1. INTRODUCTION In power system, power factor and harmonics plays very important role. For optimum utilization of available power the reactive power consumption should be reduced or nullified i.e. power factor should be unity. As we know the most of industrial load is inductive which causes the production of low power factor and harmonics respectively. Power factor correction (PFC) is a technique of counteracting the undesirable effects of electric loads that create a power factor that is less than one. Power factor correction maybe applied either by an electrical power transmission utility to improve the stability and efficiency of the transmission network or correction may be installed by individual electrical customers to reduce the costs charged to them by their electricity supplier. For stable load the fixed KVAR compensation is required, while for variable load the KVAR requirement also changes as per the load duration cycle, thus in such cases the automatic power factor control panel is required. 1.1 POWER FACTOR In general power factor is the capacity of the equipment to do the work. In electrical field, it is another form of energy which is transferred in per unit time. In AC circuits we have inductor and capacitor as components. Inductor stores energy in magnetic energy form where as capacitor stores in electrostatic energy form. None of them dissipates it. Further there is phase shift of 900 between voltage and current, but the circuit containing resistor (R), inductor (L), capacitor (C) has some phase difference angle between voltage and current. And the cosine of this angle (angle between voltage and current) is known as power factor. The value of the power factor will be always between 0 to, which represents the fraction of total power that is used to do the useful work. Causes of low power factor i. Single phase and three phase induction motor ii. Varying load in power system iii. Industrial heating furnaces iv. Electrical discharge lamps, Arc lamps v. Transformers vi. Harmonic currents Effect of low power factor i. Increase in losses ii. Large KVA rating, size of electrical equipment iii. Greater conductor size and cost iv. Poor voltage regulation and large voltage drop v. Penalty from electric power supply company on low power factor Methods for improvement of power factor i. Static capacitor bank ii. Synchronous condenser iii. Phase advancer The most commonly used method for power factor improvement is the static capacitor bank. 1.2 HARMONICS It is a component of a periodic wave having a frequency that is an integral multiple of the fundamental power line frequency. Due to contribution of all harmonics present in the system distribution of wave occurs and total harmonic distortion can be calculated. There are two types of harmonics one is characteristic harmonics and other is non-characteristic harmonics. 1. Characteristic harmonics It is a signal or wave having integral multiple of frequency of the fundamental signal or wave. It can be calculated by following equation H = (n × p) ± 1 2. Non-characteristic harmonics
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 02 Issue: 01 | Jan-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET.NET- All Rights Reserved Page 163 It is a signal or wave having other than characteristic harmonics which are not integral multiple of fundamental frequency is known as non-characteristic harmonics. Causes of harmonics i. Use of power electronic devices ii. Variable frequency drives iii. Linear and non-linear loads Effects of harmonics Harmonics present in the system will affect the following things i. Conductor overheating ii. Capacitors iii. Fuses and circuit breakers iv. Transformer v. Generators vi. Utility meters vii. Drives or power supplies viii. Computer and telephones Methods for suppressing harmonics i. No load ii. DC choke iii. Line reactor iv. 12-pulse converter v. 12-pulse distribution vi. Harmonic trap filter vii. Broadband filters Mostly filter are used for harmonics reduction. 1.3 CALCULATION OF CAPACITOR VALUE Calculation of power factor from current and required power value. Active current Im =current value *actual power factor Active current I=I*required power factor I=Im/required power factor Reactive current Im=Current value*sinǾa Reactive current I=I*sinǾr Ic=Reactive component of current Im – Reactive component current I Ic=V/Xc 1/Xc=2*Π*f*c Ic=V*2* Π*f*c 2. APFC RELAY For optimum utilization of available power the reactive power consumption should be reduced means power factor should be unity , hence, most of the Power Distribution companies have policy to penalize the industrial and commercial consumers for not maintaining power factor above certain limit i.e. above 0.90 value. 1. Need for Automatic Power Factor Correction Normally there is varying power demand on the supply system. Therefore power factor also varies as a function of the load requirements and it is difficult to maintain a consistent power factor by use of fixed compensation i.e. fixed capacitors. When there is leading power factor under light load conditions (fixed compensation) results in over voltages, saturation of transformers and so the industry penalties by electric supply authorities. Where in APFC due to automatically variation, without manual intervention, the compensation to suit the load requirements, leading power factor will be also prevented. However, due to reactive power drawn by capacitive or inductive load in the consumer premises the power factor is either lagging or leading, thus to maintain it within limit i.e. for compensating or supplying required KVAR, the capacitors or reactors in case lagging or leading PF are connected across the system. Therefore for the variable load the APFC panel is installed. The major components of APFC panel comprises of capacitor or inductor segregated in various stages, Power Factor control Relay and contactors (ON/OFF). The APFC relay monitors the various electrical parameters such as KVAR requirement, Power factor, Voltage, Current and Power consumption, of the system and uses its intelligence to control the parameters within required limit. Thus by sensing actual voltage and current of the system the APFC relay computes the system power factor and KVAR requirement, and by the control signal relay connects/disconnects the capacitor bank to the system with the help of contactors. 2.1 HARMONIC FILTER Capacitor bank connected with an inductor in order to reduce the harmonic effects. This combination constitutes a filter for harmonics. Previously, to avoid the negative effects of resonance, we have to insert an inductor in series with capacitor. But it is possible to think of placing in a point of the combination of an inductor and capacitor well dimensioned in order to get same resonance frequency for eliminating the harmonic current
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 02 Issue: 01 | Jan-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET.NET- All Rights Reserved Page 164 In this way combination of inductor-capacitor presents a very low reactance in order to harmonics eliminated which shall circulate in the assembly without affecting the whole network. This filter is called as “passive filter”. They are defined on a case basis, according to particular harmonic is filtered and they are cost effective and easy to be connected into the function. “Active filter” are instead automatically eliminate the current harmonics present in the network in wide range of frequency. They can inject a system of harmonics which is able to which neutralize those present in the network. The active filter has an advantage that filtering simultaneously dozens of harmonics as well as it does not involve design cost for dimensioning. A. CAPACITOR BANK Capacitors are used to cancel the lagging current effects. Capacitor also can reduce system losses as well as help to provide voltage support. Another one benefit of capacitor is they can reduce the total current flowing through a wire, therefore leaving capacity in the conductors for additional load. Capacitor banks can be switched manually, automatically locally. For example, system control centers operator switch capacitor bank on and off to meet load requirements or system stability reactive power demand requirements. By using capacitive support we can maintain the good system voltage and reduce the system losses as well as maintain the power factor. B. CONTACTORS A contactor is a electrically controlled switch, and it is used for switching a power circuit. A contactor is a very heavy duty so relay used for switching magnitude. Alloy containing silver is used for high current contacts. The unavoidable arcing causes the contacts to oxidize and silver oxide is still a good conductor. The overload sensing devices are a form of heat operated relay where a coil heats a bi-metal strip, or where a solder pot melts, releasing a spring to operate auxiliary contacts. These auxiliary contacts are in series with the coil. If the overload senses excess current in the load, the coil is de-energized. Contactor relays can be extremely loud to operate, making them unfit for use where noise is a chief concern. UA contactors are used for the switching of capacitor banks. For capacitor banks inrush current do not exceed 100 times the rated current. The capacitors must be discharged. And in this case their electrical life corresponds to 100,000 operations. A and AF contactors are also suited for capacitor bank switching with peak currents lower than 30 times the rated current. C. MCB A circuit breaker is an automatically operated electrical switch. It used to protect an electrical circuit from damage caused by overload or short circuit. Its basic function is to detect fault condition and, by interrupting continuity, to immediately discontinue electrical flow. Unlike a fuse, which operates once and then must be replaced, a circuit breaker can be reset to resume normal operation. 3. CONCLUSIONS The proposed single-phase and three-phase automatic power factor correction system has certain reactive current or reactive power ratings. The proposed system performs better than the traditional methods in mitigating harmonics and power factor improvement. REFERENCES [1] A. R. Shete, A. R. Thorat, “The case study of automatic power factor controller on distorted system with overview of harmonics reduction technique.” [2] IEEE Guide for application of shunt power capacitors, IEEE Std. 1036-1992, 1992. [3] T. A. Short, Electric power distribution handbook, second edition, CRC press. [4] Jain Sandesh, Thakur Shivendra Singh and Phulambrikar S.P., “Improvent power factor and Reduce Harmonics Distortion of the system”, Research Journal of Engineering Sciences, November 2012. [5] V. K. Mehta, Rohit Mehta, “Principle of power system”, Revised edition, 2008. [6] Miller T. J. “Reactive power control in Electric System”, John Willey & Sons [7] Roger C. Dugan, Mark F. Mcgranaghan, surya Santos and H. Wayne Beaty, “Electrical power system Quality”, Tata McGraw Hills publications [8] Sreenivasa reddy mulla , “Power Factor Correction”, IJIES, ISSN:2319-9598, vol. 1,Issue:- 12 November 2013. [9] Mr. A. K. Tiwari, Mrs. D. Sharma, Mr. V. K. Sharma. “Automatic power factor correction using capacitive bank”, IJERA, ISSN: 2248-9622, vol. 4, issue 2 (version 1), February 2014, pp. 393-395. [10] www.wikipedia.com
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 02 Issue: 01 | Jan-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET.NET- All Rights Reserved Page 165 BIOGRAPHIES Pratiksha K. Kurundwade is a student B.Tech in Electrical engineering department, Rajarambapu Institute of Technology, Sakharale, Rajaramnagar, Maharashtra, India. Geetanjali V. Swami is a student B.Tech in Electrical engineering department, Rajarambapu Institute of Technology, Sakharale, Rajaramnagar, Maharashtra, India. Rajanikant A. Metri is Assistant Professor in Electrical engineering department, Rajarambapu Institute of Technology,Sakharale, Rajaramnagar, Maharashtra, India. He has completed his post- graduation from College of Engineering, Pune (CoEP). He has 4 years of teaching experience and one year of industry experience. He has 05 publications in various National and International Conference and Journals. His research area is non-linear control and sliding mode control. Snehal B. Patil is a student B.Tech in Electrical engineering department, Rajarambapu Institute of Technology, Sakharale, Rajaramnagar, Maharashtra, India. Pallavi B. Patil is a student B.Tech in Electrical engineering department, Rajarambapu Institute of Technology, Sakharale, Rajaramnagar, Maharashtra, India. Madhuri . Patil is a student B.Tech in Electrical engineering department, Rajarambapu Institute of Technology, Sakharale, Rajaramnagar, Maharashtra, India.