Power Factor Correction

POWER FACTOR CORRECTION

Presented by: Katlego Mohlala and : Stalin M Ndlovu

: 920316383 : 200603148

POWER FACTOR CORRECTION Table of Contents 1.

Objective ............................................................................................................................. 3

2.

Power Factor Correction ...................................................................................................... 3

3.

Requirements ...................................................................................................................... 3

4.

Apparatus............................................................................................................................ 4

5.

Method ............................................................................................................................... 4

6.

Results and Calculations ...................................................................................................... 5

7.

Discussion ......................................................................................................................... 10

8.

Conclusion......................................................................................................................... 10

Table of figures Figure 1: circuit before correction ................................................................ 4 Figure 2: simplified circuit before correction ............................................... 4 Figure 3: Phasor diagram at lagging power factor (before correction) .......... 6 Figure 4: Measured power factor (time delay) ............................................. 7 Figure 5: Phasor diagram after power factor correction ................................ 8 Figure 6: measured voltage and current after correction ............................... 9

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION 1. Objective To perform power factor correction on a circuit with resistor and inductors.

2. Power Factor Correction The topic of power factor correction is similar to that of matching a transmission line; it is of at most importance to match the transmission line such that there are no reflections from the load back to the source. While power factor correction looks at the situation from the current point of view. Industrial loads consist of heavy inductive machines and long cables. Due to the inductive nature of the circuit reactive power will results because the more the inductance the more current required for the same power that can be delivered by a none inductive load. Ztotal = R+jXl; impedance of the circuit. Ө=arctan

Xl 𝑅

=pf; power factor angle.

If pf<1 lagging (inductor dominates). If pf>1 leading (capacitor dominates). Pf=1; unity (equal compensation between inductor and capacitor i.e. no reactive power). The lack of a good power factor can result in huge losses in both the equipment and the transmission lines in power systems, this can be a huge economical strain for any Power distribution utility like Eskom

3. Requirements  

To design a circuit with a lagging power factor. To correct the power factor of the circuit close to unity.

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION 4. Apparatus 

2 Isolators



LCR meter



Multi-meter



The orange box



Oscilloscope

5. Method Input voltage: 40V Input frequency 50Hz

Figure 1: circuit before correction

Figure 2: simplified circuit before correction

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION

6. Results and Calculations Theoretical (determined by using circuit parameters) Vin  40Vrms Total  Im pedance Z  R  JX l Z  333 .3  j 232 .5 Z  406 .1334 .9 0 

Current drawn by components.

I in 

Vin 400 0   98.5  34.9 0 mA Z 406 .1334.9 0

Power factor angle pf  cos  cos 34 .9  0.82 Lagging

The power factor is however large but this does not stop us correcting power factor. We are looking at a practical purpose and we aimed for unity. 

From the power factor angle we can decrease the current drawn by the inductor by increasing the power factor as close to unity as possible. This was for experimental purpose thus we can aim for unity “ideal situation”.

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION Complex Power S  P  jQ S  VI *





S  40 0.0985 34 .9o VA S  3.232  j 2.256VA P  3.323W Q  2.256VAR S  3.94 34 .9o VA

Figure 3: Phasor diagram at lagging power factor (before correction)

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION

Measured power factor

Figure 4: Measured power factor (time delay)

𝜽=

𝒕𝒊𝒎𝒆 𝒅𝒆𝒍𝒂𝒚 𝒑𝒆𝒓𝒊𝒐𝒅

× 𝟑𝟔𝟎° =

𝟐.𝟐𝟎 𝟐𝟎

× 𝟑𝟔𝟎° = 𝟑𝟗. 𝟔°

Power factor was calculated to be: pf=cos39.60=0.77 lagging The difference between the theoretical calculation and the actual measured power factor is 0.05. the difference is quite small and we can neglect it.

Power factor correction Required capacitance for correction Ideally we want the power factor to be 1, thus we correct our power factor to 0.95 lagging. This will give a new angle between the voltage and current.

 new  cos1 0.95  18.2o At this new power factor we can approximate the capacitive effect that will be introduced in the circuit to compensate for the impressed current in the inductors.

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION The resulting capacitive reactive power is as follows:

 new  P tan new Qnew  3.232 tan18 .2 0 Qnew  1.063VAR  Qc  Q  Qnew  2.256  1.063  1.193VAR  Zc 

V

2

S*



40 2  1341 .2 1.193

but C j

1 1 j  2.4 F 2fZ c 2  50  1341 .2

S new  3.232  j1.193VA S new  3.4520 .30 VA I new 

* S new 3.45  20 .30   86 .25  20 .30 mA 0 Vin 40 0

 new  20 .30 P  Pnew  3.232W Qc  1.193VAR

Figure 5: Phasor diagram after power factor correction

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION

Measured power factor after correction

Figure 6: measured voltage and current after correction

The time delay between voltage and current was measured to be 1.12ms

𝜽 𝒏𝒆𝒘 =

𝒕𝒊𝒎𝒆 𝒅𝒆𝒍𝒂𝒚 𝟏. 𝟏𝟐 × 𝟑𝟔𝟎° = × 𝟑𝟔𝟎° = 𝟐𝟎. 𝟐° 𝒑𝒆𝒓𝒊𝒐𝒅 𝟐𝟎

Pf=cos20.20=0.94

Stalin M Ndlovu and Katlego Mohlala

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POWER FACTOR CORRECTION 7. Discussion From the above results it can be seen that;  When correcting the power factor the time delay between the current and voltage is reduced.  The reduced time delay reduces the phase angle i.e. as the phase angle approaches zero the power factor approaches unity.  The current is always lagging the voltage this is of significant importance as it reduces distortions.  In power factor correction for a single phase circuit as in figure1 it can be shown that there is a reduction in the current drawn by the circuit when a capacitor is introduced in parallel to the load. This was achieved as the current dropped from 98.5mA to 86.25mA

8. Conclusion

The objective of power factor correction is to attain a power factor close to unity. The importance of this power factor is to remove all the reactive energy which is oscillatory. In our design and experiment for power factor correction we corrected the power factor to 0.94 instead of unity in order to keep little reactive energy for stability.

Stalin M Ndlovu and Katlego Mohlala

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