# الموضوع: Power Factor Correction

1. ## Power Factor Correction

Power Factor Correction

Many loads are highly inductive, such a lightly loaded motors and illumination transformers and ballasts. You may want to correct the power factor by adding parallel capacitors. You can also add series capacitors to "remove" the effect of leakage inductance that limits the output current.

Why correct the power factor?

The current flow through the circuit is increased by the reactive component. Normally, loads are represented by a series combination of a resistance and a purely imaginary reactance. For this explanation, it is easier to contemplate it as an equivalent parallel combination. .
The current through the reactive component (Ireactive) dissipates no power, and neither does it register on the watt hour meter. However, the reactive current does dissipate power when flowing through other resistive components in the system, like the wires, the switches, and the lossy part of a transformer (Rline). Switches have to interrupt the total current, not just the active component. Wires have to be big enough to carry the entire current, etc. Correcting the power factor reduces the amount of oversizing necessary.

Correcting power factor
Given the reactive load component (Xload), you can calculate the capacitance that would be put in parallel to exactly match it using the equation:

Xc = 1/ (omega C) = 1/(2 *pi * f * C)
for 60 Hz: Xc = 1/( 2*pi * 60* C) =1/ (377*C)

or, rearranging: C = 1/(377*Xc)

Power factor correction capacitors are often rated in kVar, instead of uF, because that is how the power company works. Say a factory has several thousand horsepower worth of motors at .85 power factor. They might have a reactive component of several hundred kVar. At a distribution voltage of 14,400 volts, this would require a capacitor with an impedance of a bit more than 1000 ohms, or about 2.5 microfarads, a reasonable sized and priced package. However, if you were crazy enough to try to compensate this at 230 volts, you would need about .01 Farads (i.e. 10,000 uF), a sizeable package.

For very large systems, even capacitors get unwieldy. One approach is to use large over excited synchronous motors which look like capacitors, electrically. Another approach is clever systems of thyristors and inductors which simulate the capactive reactance by drawing "displacement current".

Classic reactive loads, like transformers, lighting ballasts, and AC motors still have a sinusoidal current flow. The phase of the current is just shifted from that of the supply voltage. However, there are some loads which draw distinctly non-sinusoidal currents. The most recently notorious is the switching power supply in a PC. These power supplies start with a bridge rectifier feeding a capacitor, and so, particularly at part load, draw their current in little peaks, when the instantaneous line voltage is above the capacitor voltage, forward biasing the rectifier. Another notorious non-sinusoidal current draw is the popular phase controlled light dimmer, which uses a TRIAC or SCR to reduce the RMS voltage to the load by turning on partway through the half cycle. Not only is the current waveform highly non-sinusoidal, but it is also out of phase with the voltage supply. Hence, these loads have a non-unity power factor, and draw reactive power.

However, to compensate these loads, you have to come up with a means to supply the reactive current at the appropriate times. A simple capacitor doesn't do this. A capacitor only compensates nice sinusoidal power factor lags, like those from linear (non-saturating) inductors.

Example of Power Factor Correction
Let's take an example. A 3/4 HP electric motor has a power factor of .85. The nameplate current is 10 Amps at 115 Volts, or 1150 Volt Amps.

Apparent power = 1150 Volt Amps
Active power (P) = .85 * 1150 = 977.5 Watts
Reactive Power (Q) = sqrt(1150^2 - 977.5^2) = 605 VAR
So, we need about 600 var of power factor correction. I'm rounding to a couple digits, because, in reality, it's unlikely that the power factor is known to more accuracy, nor will any of the PFC components be that precise. (10% accuracy would be quite good for a capacitor). Now, assume we want to put the capacitor in parallel with the motor: Calculating the required impedance from Q = E^2/X, where Q is the reactive power needed:

600 = 115^2/X => X = 115^2/600 = 22 ohms (rounding to 2digits)
C = 1 /( 2 * pi * f *X) = 1/ (377 * 22) = 120 uF (again, rounding to 2 digits)
which is a fairly large capacitor in a constant duty environment (i.e. motor run, as opposed to motor start, where the capacitor is only in the circuit for a short time). You can calculate the RMS current through the capacitor either by dividing the VARs by the line voltage (600/115) or by dividing line voltage by reactance (115/22); both come out at around 5 1/4 Amps, so you'd want a capacitor rated at somewhat more current (e.g. 7-10 A). The capacitor's series resistance should be pretty low, or it will dissipate a fair amount of energy. If the dissipation factor were 1%, you'd be dissipating about 6 Watts in the capacitor.

One can also put the PFC capacitor in series with the load. In this case the capacitor would carry the entire load current of 10A, but, the required value is different. For a series compensation, you'd determine the series equivalent of the load (we used a parallel model, above). For the series model, you use currents, instead of voltages:

600 VAR = I^2 * X => 600 = 10*10 * X => X = 6 ohms

And converting an impedance to a capacitance: C=1/(377*6) = 440 uF.

So, not only would the capacitor be larger, but it would need to carry the entire load current. For this example, at least, parallel PFC seems to be a better approach. Only if the power factor were very poor, so the reactive impedance was quite large (and the corresponding capacitance low) would series compensation seem to be useful.

If the line voltage were higher, the correction impedance would be increased as the square of the line voltage. The capacitance would be reduced as the square of the line voltage. That is, if the same motor were run off 230 Volts, the capacitor would only need to be about 30 uF. And if we were to do power factor compensation at the distribution voltage of 4160 volts (for example), you would only need about .1 uF. This is why power factor correction is usually done in the distribution network at MV or HV, and not at the end voltage.

2. ## رد: Power Factor Correction

شكراً لك اخي الحبيب / دكتور // على

3. ## رد: Power Factor Correction

شكرا استاذي الفاضل موسى لهذا المرور الكريم..بارك الله فيك

4. ## رد: Power Factor Correction

جزاك الله خير الجزاء

موضوع هام بالفعل

5. ## رد: Power Factor Correction

شكرا استاذ ناصر على مروركم الكريم

6. ## رد: Power Factor Correction

شكرا مهندس على بارك الله فيك
نحتاج مجهودات رجال مثلك لاثراء قسم الجوده فى المنتدى خاصه انى مهندس جوده بهيئه كهرباء مصر
ولكن سؤال لماذا حسبت المكثف للموتور على الحمل الكامل للموتور full load علما بان معظم المواتير لا تعمل بالحمل الكامل كما انك لم توضح نوع المكثف ثابت ام متغير على مراحلsteps with regulator

7. ## رد: Power Factor Correction

اخي العزيز استاذ ايمن: ان موضوع تحسين معامل القدرة وبالتالي تقليل خسائر القدرة موضوع متشعب و مهم و ينقسم بصورة رئيسية و حسب طبيعة الاستخدام الى فرعين رئيسين اولهما هو استخدامات تحسين معامل القدرة في نظام القوىو القدرة الكهربائية..و في هذا الحقل تكون القدرة السعوية او الحثية المضافة (capacitive or inductive power in other words reactive power) كبيرة جدا مقارنة مع الاستخام الثاني في المكائن و المحركات...حيث انه في نظام القدرة نحتاج بعض الاحيان مثلا في النهار الى اضافة احمال سعوية( for lagging power factor) على الشبكة لكي تعادل الاحمال الحثية الرئيسية في احمال المدن الكبيرة و المعامل الضخمة...اما في الليل فاغلب المصانع تتوقف وفي بعض الاوقات من السنة يصبح لدينا تقدم في التيار (leading power factor) و هذا يتطلب دخول احمال حثية على الشبكتبين طبيعة الحاجةة... و من هنا تتبين طبيعة الحاجة اما لمكثف او لمحاثة لتحسين معامل القدرة و تقليل الزاوية بين الفولتية و التيار...لذا و بما ان احمال الشبكة كبيرة و تتغير ضمن مدى كبير فاننا نحتاج الى مكثفات متغيرة و تغيرها يتناسب مع تغير معامل القدرة لذا فان انسب حل لذلك هو ربط محركات تزامنية (synchronous motor) وهذه تقوم مقام المكثفات الثابتة المضافة....و هنالك طرق جديدة و ذكية في تحسين معامل القدرة عن طريق استخدام الثايرسترات و الكترونيك القوى ومن خلال استخدام السيطرة الذكية في دوائر التحكم بزوايا الاشعال باستخدام المسيطرات الذكية و الحديثة و الرئيسية منها هي ( Fuzzy logic controller, genetic algorithms and neural controller ) هذا المجال التطبيقي في نظام القوى ... اما المجال الثاني و الذي لايقل اهمية من الاول فهو تحسين معامل القدرة في مناطق الاحمال نفسها كالمكائن و المحركات و ممكن تطبيق نفس التقنيات المذكورة سابق و لكن باحجام اصغر تتناسب مع طبيعة الحمل..... اتمنى ان اكون قد وضحت ...مع حبي و تقديري

8. ## رد: Power Factor Correction

As an answer for your question again, any engineer take the worest case in his design ,so he must take the full load condition , but nowady in the modern machine control the value of the compensating capacitor vary with the delay angle of the machine current, so the modern and intelligent control had been taken into account in such designes.

9. ## رد: Power Factor Correction

مهندس على شكرا لك شكرا جزيلا
تقبل تحياتى

10. ## رد: Power Factor Correction

مشكور ورائع دائما د.علي البكري ولكم تحياتي.

11. ## رد: Power Factor Correction

شكرا...اساتذه على هذا المرور الرائع و الكلمات المشجعة مع الحب و التقدير

12. ## رد: Power Factor Correction

جزاك الله خيرا

13. ## رد: Power Factor Correction

مشكور اخي العزيز دكتور علي البكري
مشاركة قيمة
تقبل خالص تحياتي

14. ## رد: Power Factor Correction

شكرا استاذ حمادة و استاذ رباح على هذا المرور الكريم...مع الحب و التقدير

15. ## رد: Power Factor Correction

شكرا ..بارك الله فيك

16. ## رد: Power Factor Correction

ارجو ان تعطونا رايكم بهذه الحاسبة عن power factor correction :
http://www.monachos.gr/eng/calculato...calculator.htm

17. ## رد: Power Factor Correction

جزاكم الله خيرا مهندس على

18. ## رد: Power Factor Correction

المشاركة الأصلية كتبت بواسطة Eng. Rabia Raslan
ارجو ان تعطونا رايكم بهذه الحاسبة عن power factor correction :
http://www.monachos.gr/eng/calculato...calculator.htm
اعتذر عن الخطأ في الرابط السابق واليكم الرابط الصحيح:

http://www.monachos.gr/en/calculator...calculator.asp

19. ## رد: Power Factor Correction

شكرا استاذنا الفاضل وجزاك الله كل الخير

20. ## رد: Power Factor Correction

شكرا لجميع الاخوة المعقبين و بارك الله فيكم

#### معلومات الموضوع

##### الأعضاء الذين يشاهدون هذا الموضوع

الذين يشاهدون الموضوع الآن: 1 (0 من الأعضاء و 1 زائر)

#### ضوابط المشاركة

• لا تستطيع إضافة مواضيع جديدة
• لا تستطيع الرد على المواضيع
• لا تستطيع إرفاق ملفات
• لا تستطيع تعديل مشاركاتك
•