COURSE Project
Subject: Electromechanical Motion Devices and
Laboratory EE323
Systems
Project Name: Power Factor Correction of an Electrical System
Group Member Names:
1
Contents
Introduction ............................................................................................................................................... 3
Available Solution .................................................................................................................................... 3
Power Factor Improvement Methods: .................................................................................................... 4
a.
Static Capacitor Bank ................................................................................................................... 4
b.
Synchronous Condensers/Over Excited Synchronous Motors ................................................... 4
c.
Phase Advancers........................................................................................................................... 5
Proposed Solution ........................................................................................................................................ 5
Calculations for improving PF from 0.30 to 0.70:.................................................................................... 6
1.
Current Load and PF calculations: ................................................................................................ 6
2.
Required Reactive Power to improve PF to 0.70: ......................................................................... 6
3.
Resultant Values of Power and Power Factor: ............................................................................. 7
Use of Synchronous Motor for PFC: ................................................................................................... 7
Synchronous Motor V-Curve..................................................................................................................... 8
Synchronous Motor operating condition to improve PF to 0.70: ............................................................. 9
Conclusion .................................................................................................................................................... 9
References ................................................................................................................................................. 9
2
Figure 1: Power Triangle ............................................................................................................................... 4
Figure 2: Use of Capacitor to improve PF ..................................................................................................... 4
Figure 3: Load connected with 415V Supply ......................................................................................... 5
Figure 4: Power Triangle before PFC ..................................................................................................... 6
Figure 5: Required Reactive Power ........................................................................................................ 6
Figure 6: Resultant Power Triangle after PFC ....................................................................................... 7
Figure 7: Synchronous Motor's V Curve ................................................................................................. 9
Table 1: Parameters of Electrical System .............................................................................................. 5
Table 2: Synchronous Motor's data ......................................................................................................... 7
Table 3: Calculated Values of Synchronous Motor ............................................................................... 8
3
Introduction
Electrical machines are the major part of any industry process system. They are also
being used in home alliances for making the hand work more easy and fast. So they are
consuming major portion of electrical energy. The most commonly machine used is called
“Induction Motor” as it is being used in a lot of applications due to its rugged design, low
maintenance, low-cost, and direct connection to an AC power source. As there are a lot of
advantages of using Induction Motors (IM), there is also an important disadvantage is the
lowering of the Power Factor. These motors effect the system’s power factor very much as due
to consumption of Reactive Power. This low Power Factor causes the higher current demand,
higher voltage drop, poor voltage regulation, more copper losses and reduction of Power Plant’s
capacity. Moreover, due to low power factor, the distribution companies make a penalty to the
bulk power consumers as they are main source of lowering the power factor.
This project task is about to enhance the lowered power factor to an allowable extent to avoid
the above said losses and disadvantages. In this lab, we will become able to:
i.
ii.
iii.
Understand the importance of Power Factor.
Understand about different methods to increase the power factor.
Know how does a Synchronous motor is used to enhance the lowered power factor.
Available Solution
There are two components of Apparent Power “S” called Active Power “P” and Reactive
Power “Q”. Power triangle is made using these components as shown in fig.1. Power
Factor is the cosine of the angle between True / Active Power “P” and Apparent Power
“S”. Active power is consumed in Resistive types of loads and Reactive Power
consumption is caused due to inductive or capacitive loading. Reactive power is not
consumed in the active work of the load but it is burden on the system and it oscillates
in the circuit. More the reactive power, higher will be the power factor angle but lower
will be the power factor. Less power factor is not desirable as it causes some critical
disadvantages in the system as described in the introduction section.
As the major load contribution in the world is the induction motors. They have high
inductance values and less resistance value. They cause to lower the power factor to a
significant lower value. Higher the KVA Power rating of the motor, higher will be the
inductance value and hence lower will be the Power Factor. Where IMs are most useful
elements in the world, they also cause for lowering the power factor.
4
Figure 1: Power Triangle
Power Factor Improvement Methods:
It has been discussed that there is dead need to improve the power factor
near unity as power factor has values between 0 and 1. For improving the
power factor to unity value, following methods are used:
a. Static Capacitor Bank
b. Synchronous Condensers/Over Excited Synchronous Motors
c. Phase Advancers
a. Static Capacitor Bank
In this method, power factor is improved using capacitor banks. They are not rotating
part and also don’t consume active power. This is the very important benefit for the use
so they are mostly used for power factor correction in the industry and in the substation.
Figure 2: Use of Capacitor to improve PF
b. Synchronous
Condensers/Over Excited Synchronous Motors
Synchronous motors are used in the industry for constant speed driven processes of the
industry. They have zero slip as their rotors are aligned up with rotating stator filed.
5
Besides using synchronous motors in the industry processes, they are also used for the
power factor correction. For using these machines as PFC purpose, they are used on
no load and their field currents are increased to have suitable power factor value.
Overexcited synchronous motors generate reactive power as required by the inductive
loads. They draw leading current form the supply and it leads the supply voltage by 90
degree angle.
They have some drawbacks also. They consume active power and they are rotating
machine and hence require wear and tear costs.
c. Phase Advancers
Phase advancer is a basic AC exciter that is associated with the shaft of the motor and
works with the motor's rotor circuit for power factor improvement. Phase advancer is
utilized to improve Power factor.
There happens lagging current in the stator windings of induction motor that is always
90° or less than 90° out of phase with Voltage. In this case, pf will be low. The solution of
this problem is to excite ampere-turns by external AC source, in this way power factor
can be improved significantly. This is done by using the phase advancers.
Proposed Solution
In this project, we have to calculate the reactive power of the system shown in fig
required to improve the power factor from a very low value of 0.30 to 0.70.
Figure 3: Load connected with 415V Supply
The load is having induction motor and synchronous motor in parallel. The overall values are:
Table 1: Parameters of Electrical System
Voltage of the 3 phase power supply
415 V
Current power factor 0.30
0.30
Required power factor 0.70
0.70
Active Power of the system 42.5 W
42.5 W
6
Calculations for improving PF from 0.30 to 0.70:
1. Current Load and PF calculations:
𝑺𝒖𝒑𝒑𝒍𝒚 𝑽𝒐𝒍𝒕𝒂𝒈𝒆 = 𝑽𝒔 = 𝟒𝟏𝟓 𝑽
𝑨𝒄𝒕𝒊𝒗𝒆 𝑷𝒐𝒘𝒆𝒓 = 𝑷𝟏 = 𝟒𝟐. 𝟓 𝑾
𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝑷𝒐𝒘𝒆𝒓 𝑭𝒂𝒄𝒕𝒐𝒓 = 𝑷𝑭𝟏 = 𝑪𝒐𝒔𝜽𝟏 = 𝟎. 𝟑𝟎
𝑷𝒐𝒘𝒆𝒓 𝑭𝒂𝒄𝒕𝒐𝒓 𝑨𝒏𝒈𝒍𝒆 = 𝐜𝐨𝐬 −𝟏 𝟎. 𝟑𝟎 = 𝟕𝟐. 𝟓𝟒°
𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝑹𝒆𝒂𝒄𝒕𝒊𝒗𝒆 𝑷𝒐𝒘𝒆𝒓 = 𝑸𝟏 = 𝑷(𝑻𝒂𝒏𝜽𝟏 )
𝑄1 = 42.5 × 𝑇𝑎𝑛(72.54°) = 135.12 𝑉𝐴𝑅
𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝑨𝒑𝒑𝒂𝒓𝒆𝒏𝒕 𝑷𝒐𝒘𝒆𝒓 = 𝑺𝟏 =
𝑷𝟏
𝟒𝟐. 𝟓
=
= 𝟏𝟒𝟏. 𝟔𝟔 𝑽𝑨
𝑷𝑭𝟏 𝟎. 𝟑𝟎
Figure 4: Power Triangle before PFC
2. Required Reactive Power to improve PF to 0.70:
𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝑷𝒐𝒘𝒆𝒓 𝑭𝒂𝒄𝒕𝒐𝒓 = 𝑷𝑭𝟐 = 𝑪𝒐𝒔𝜽𝟐 = 𝟎. 𝟕𝟎
𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝑷𝒐𝒘𝒆𝒓 𝑭𝒂𝒄𝒕𝒐𝒓 𝑨𝒏𝒈𝒍𝒆 = 𝜽𝟐 = 𝐜𝐨𝐬 −𝟏 𝟎. 𝟕𝟎 = 𝟒𝟓. 𝟓𝟕°
𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝑹𝒆𝒂𝒄𝒕𝒊𝒗𝒆 𝑷𝒐𝒘𝒆𝒓 = 𝑸 = 𝑷𝟏(𝑻𝒂𝒏 𝜽𝟏 − 𝑻𝒂𝒏 𝜽𝟐 )
𝑸 = 𝟒𝟐. 𝟓(𝑻𝒂𝒏 𝟕𝟐. 𝟓𝟒° − 𝑻𝒂𝒏 𝟒𝟓. 𝟓𝟕°) = 𝟗𝟏. 𝟕𝟕 𝑽𝑨𝑹
Figure 5: Required Reactive Power
7
3. Resultant Values of Power and Power Factor:
After the power factor improvement;
𝑵𝒆𝒘 𝒑𝒐𝒘𝒆𝒓 𝒇𝒂𝒄𝒕𝒐𝒓 = 𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝑷𝒐𝒘𝒆𝒓 𝑭𝒂𝒄𝒕𝒐𝒓 = 𝑷𝑭𝟐 = 𝑪𝒐𝒔𝜽𝟐 = 𝟎. 𝟕𝟎
𝑵𝒆𝒘 𝑷𝒐𝒘𝒆𝒓 𝑭𝒂𝒄𝒕𝒐𝒓 𝑨𝒏𝒈𝒍𝒆 = 𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝑷𝒐𝒘𝒆𝒓 𝑭𝒂𝒄𝒕𝒐𝒓 𝑨𝒏𝒈𝒍𝒆 = 𝜽𝟐 = 𝐜𝐨𝐬 −𝟏 𝟎. 𝟕𝟎 = 𝟒𝟓. 𝟓𝟕°
𝑹𝒆𝒔𝒖𝒍𝒕𝒂𝒏𝒕 𝑹𝒆𝒂𝒄𝒕𝒊𝒗𝒆 𝑷𝒐𝒘𝒆𝒓 = 𝑸𝟐 = 𝑸𝟏 − 𝑸 = 𝟏𝟑𝟓. 𝟏𝟐 − 𝟗𝟏. 𝟕𝟕 𝑽𝑨𝑹
𝑸𝟐 = 𝟒𝟑. 𝟕𝟓 𝑽𝑨𝑹
𝑹𝒆𝒔𝒖𝒍𝒕𝒂𝒏𝒕 𝑨𝒄𝒕𝒊𝒗𝒆 𝑷𝒐𝒘𝒆𝒓 = 𝑷𝟐 = 𝑷𝟏 = 𝟒𝟐. 𝟓 𝑾
𝑹𝒆𝒔𝒖𝒍𝒕𝒂𝒏𝒕 𝑨𝒑𝒑𝒂𝒓𝒆𝒏𝒕 𝑷𝒐𝒘𝒆𝒓 = 𝑺𝟐 =
𝑷𝟐
𝟒𝟐. 𝟓
=
= 𝟔𝟎. 𝟕𝟏 𝑽𝑨
𝑷𝑭𝟐 𝟎. 𝟕𝟎
Figure 6: Resultant Power Triangle after PFC
Use of Synchronous Motor for PFC:
As stated before, synchronous motors are also used for improving the power factor.
Synchronous motor filed current is increased to increase the injective reactive power and also
the power factor. This machine is used in spite of capacitor bank so to enhance the power factor
to a desired value. Below table 2, is about the synchronous motor data that us showing about
motor parameters by changing field current.
Table 2: Synchronous Motor's data
Synchronous Motor's Data
Sr# I2(dc) E1(AC) I1(AC)
P
1
0.00 415.00 0.371 40.00
2
0.10 415.00 0.209 30.00
3
0.20 415.00 0.093 20.00
4
0.30 415.00 0.028 10.00
5
0.40 415.00 0.016 5.00
6
0.50 415.00 0.008 3.00
7
0.60 415.00 0.030 7.00
8
0.70 415.00 0.042 12.00
9
0.80 415.00 0.089 18.00
10 0.90 415.00 0.278 31.00
8
To find synchronous motor’s apparent power, reactive power and power factor values, following
formulas have been used and the results have been recorded in table 3.
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟 = 𝑆 = 𝑉 × 𝐼
𝑅𝑒𝑎𝑐𝑡𝑖𝑣𝑒 𝑃𝑜𝑤𝑒𝑟 = 𝑄 = √𝑆 2 − 𝑃2
𝑃𝑜𝑤𝑒𝑟 𝐹𝑎𝑐𝑡𝑜𝑟 = 𝑃𝐹 =
𝑃
𝑆
Table 3: Calculated Values of Synchronous Motor
Synchronous Motor's Data
Sr# I2(dc) E1(AC) I1(AC)
P
S
Q
PF
1
0.00 415.00 0.371 40.00 153.97 148.68 0.26
2
0.10 415.00 0.209 30.00 86.74
81.38 0.35
3
0.20 415.00 0.093 20.00 38.60
33.01 0.52
4
0.30 415.00 0.028 10.00 11.62
5.92
0.86
5
0.40 415.00 0.016 5.00
6.64
4.37
0.75
6
0.50 415.00 0.008 3.00
3.32
1.42
0.90
7
0.60 415.00 0.030 7.00
12.45
10.30 0.56
8
0.70 415.00 0.042 12.00 17.43
12.64 0.69
9
0.80 415.00 0.089 18.00 36.94
32.25 0.49
10
0.90 415.00 0.278 31.00 115.37 111.13 0.27
Synchronous Motor V-Curve
Power factor of synchronous motor can be controlled by varying the filed current. As it can be
seen from table 3, field current I2 (dc) is varied from 0.00 to 0.90 A, machine’s armature current
I1 (AC) started decreasing till sr#6. At that point, power factor is made 0.90. After that more
excitation will lower the PF in the leading manner.
Synchronous “V” curve is used to represent armature current variation with change of field
current at different load conditions. In this project, machine is operating at no load and V curve
is drawn as shown in fig 7. It is clearly shown that by increasing field current, armature current is
lowered. But after field current of the value 0.50 A (dc), the armature current has started to
increase and hence power factor is also lowered in leading.
9
Armature Current Ia
Synchronous Motor's "V" Curve
0,400
0,300
0,200
0,100
0,000
0,00
0,20
0,40
0,60
0,80
1,00
Field Current If
Figure 7: Synchronous Motor's V Curve
Synchronous Motor operating condition to improve PF to 0.70:
As calculated in the calculation section, required reactive power for improving pf to a value of
0.70 was determined to be 91.77 VAR having unity PF.
Synchronous motor can improve the power factor to 0.70 value it will provide KVAR value near
to 91.77 VAR at unity PF. But looking at table 3, both conditions have not been met. As in sr#2,
Q will is 81.38 but with low pf of 0.35. So motor is consuming this reactive power not generating.
But in sr#6, power factor is good of value 0.90 but with very low reactive power. So for
enhancing the pf to 0.70, the synchronous machine should generate the required reactive power
with pf near to unity.
Conclusion
In this project, concept of power factor has been understood clearly. Power factor importance,
causes of lowering pf and how to improve pf has been demonstrated in detail. Concept of power
triangle was discussed and its components active, apparent and reactive were drawn and
understood briefly .Methods of power factor improvement such as capacitor banks, synchronous
condensers and phase advancers were discussed shortly. Power factor improvement from 0.30
to 0.70 value of a given electrical system was has been done using manual mathematical
calculations step by step. At the end, power factor improvement using synchronous motor has
been studied and observed using a given data of the said machine that was connected in
parallel with the induction motor.
References
1. García, O., Cobos, J.A., Prieto, R., Alou, P. and Uceda, J., 2003. Single phase power
factor correction: A survey. IEEE Transactions on Power Electronics, 18(3), pp.749-755.
2. Todd, P.C., 1999. UC3854 controlled power factor correction circuit design. UNITRODE
application note U-134, pp.10-303.
3. Bhattacharyya, S., Choudhury, A. and Jariwala, P.H., 2011. Case Study On Power
Factor Improvement. International Journal of Engineering Science and Technology
(IJEST), 3(12), pp.837-8378.
10
4. Khanchi, S. and Garg, V.K., 2013. Power factor improvement of induction motor by using
capacitors. International Journal of Engineering Trends and Technology (IJETT), 4(7),
pp.2967-2971.
5. Al-Hamrani, M.M., Von Jouanne, A. and Wallace, A., 2002, June. Power factor
correction in industrial facilities using adaptive excitation control of synchronous
machines. In Conference Record of the 2002 Annual Pulp and Paper Industry Technical
Conference (Cat. No. 02CH37352) (pp. 148-154). IEEE.
6. Vartanian, R., Toliyat, H.A., Akin, B. and Poley, R., 2012, February. Power factor
improvement of synchronous reluctance motors (SynRM) using permanent magnets for
drive size reduction. In 2012 Twenty-Seventh Annual IEEE Applied Power Electronics
Conference and Exposition (APEC) (pp. 628-633). IEEE.