# Power Factor Correction Capacitors Sizing Calculations – Part Eleven

Today, we will start explaining Different Methods of Calculations for PF correction capacitor Ratings.
As we explained before in article Power Factor Correction Capacitors Sizing Calculations – Part Four”, that the Types of Power Factor Correction Capacitors according to Location can be categorized to:
1. Central Compensation,
2. Individual Compensation,
3. Group Compensation,
4. Hybrid Compensation.
Today, we will start explaining how to calculate the capacitor KVAR rating for above types of compensation.

 Factors Affecting The Rated KVAR For a Capacitor

 Before we start explanation of different methods for Calculation of the Capacitor KVAR Rating, we must know the (2) factors which affect the Rated KVAR for a capacitor; the frequency and voltage. Standard capacitor ratings are designed for 50 or 60Hz operation. When operated at less than nameplate frequency of 50 or 60Hz, the actual KVAR attained will be less than rated KVAR. Also, If the operating voltage is less than the rated voltage, a reduction in the nameplate KVAR will be realized. The following equation defines the relation:   C = KVAR / (2Πf E2 X 10-3 ) Or in another way: KVAR=2f ΠCE2 X 10-3   Where:   C = capacitance in Farads KVAR= reactive power Π = 3.1416 E = network voltage in KV f = network frequency in Hz

 Calculation of the Capacitor KVAR Rating for Compensation at Transformer

 A transformer consumes reactive power to ensure that its windings are magnetized. We have (3) methods to calculate the capacitor KVAR rating for Compensation at Transformer as follows: Using Equation, Using Tables, Using Rule Of Thumb.

 Method#1: Using Equation The capacitor KVAR rating for Compensation at Transformer can be calculated from the following equation:       Where: i0% : the percentage no-load current, uk% : the percentage short-circuit voltage, Pfe  : the iron losses, Pcu : the copper losses. KL: the load factor, defined as the ratio between the minimum reference load and the rated power of the transformer. The above data can be derived from the nameplate characteristics of the transformer.   Example#1:   Assume that the power factor of a 630 kVA oil distribution transformer which supplies a load equal to 60% of its rated power is to be corrected.   Calculate the capacitor KVAR rating for Compensation at Transformer.   Solution:   From the nameplate characteristics of the transformer: i0% = 1.8% uk% = 4% Pcu = 8.9 kW Pfe = 1.2 kW The compensation power of the capacitor bank connected to the transformer shall be:

 Method#2: Using Tables Table-1 in below shows the reactive power of the capacitor bank Qc [kvar] to be connected to the secondary winding of a transformer according to the different foreseen load level. In particular, the reactive compensation power shall vary following a quadratic law with respect to the load coefficient of the transformer.       Table-1   Example#2:   From Table-1, For an 630 kVA oil distribution transformer with load factor equal to 0.5, the necessary compensation power is 17 kvar.

Method#3: Using Rule Of Thumb
The below rule of thumb gives Approximate estimates for the required reactive capacitor rating for compensation at transformer as follows:

 Consumer Capacitor rating Transformers with individual PFC 2.5% of transformer capacity 5% for older transformers Transformers with Central PFC 25 – 33% of transformer capacity when aiming for cos ϕ = 0.9 40 – 50% of transformer capacity when aiming for cos ϕ = 1

 Two important notes must be checked when connecting PFC capacitors to the transformer terminals:   Check for resonance between transformer and capacitor, Checking the "No Load" Voltage Rise.

 A- Check for Resonance between Transformer and Capacitor

 The resonant frequency can be calculated from the following formula: f = fp √(Psc/Pc) f = resonant frequency, fp = power frequency, Psc = short circuit power of the transformer (kVA), Pc = power of the capacitor (kVAR).   If the frequency obtained is too close to that of a harmonic, the value of the capacitor rating should be modified. Most common harmonic frequencies, 3rd, 5th, 7th, etc...   Example#3: for the following transformer: S = 630 KVA Usc = 6% P = 500 KW Qc = 275 kVAr Calculate the resonant frequency.   Solution:   The short-circuit power is: Ssc = S x 100 / Usc = 630 x 100 / 6 = 10500 KVA   The resonance frequency will therefore be: f = fp √(Psc/Pc) = 50 x √(10500/275) = 308.96 Hz The system will resonate at order n = f/ fp = 6.18

 B- Checking the "No Load" Voltage Rise

 This step is used to check that if the Voltage Constraints Met or not. The basic reason why many plants cannot leave fixed capacitors energized continuously is that the voltage increases too much when the load is low. The limit on the steady state voltage is generally about 110%. Above this limit, the transformers will saturate and become overheated. Of course, the life of incandescent lamps is also drastically reduced. If we assume that the normal system voltage could be a 105%, then the capacitors should cause no more than a 5% rise at no load. For simple cases, the percent voltage rise, ΔV, can be estimated from the kvar of the capacitor and the percent impedance, Z, and kVA ratings of the main transformer as follows: %ΔV = (Kvar x %Z) / KVA Example#4: Calculate the voltage rise that will result from applying a 350 kvar capacitor at the secondary of a 1000 kVA transformer with an impedance of7%. Solution: %ΔV = (Kvar x %Z) / KVA %ΔV = 350 x 7 / 1000 = 2.45% Also, from the following curve (fig.1) you can find the % voltage drop for any power factor improvement.       Fig.1     Example#5:   Improve power factor from 60 percent to 90 percent, calculate the reduction in voltage drop.   Solution:   From the above curve, at PF = 0.6 the, Voltage drop = 5.1% And at PF = 0.9, the voltage drop = 3.6% So, the reduction in voltage drop = 5.1-3.6 = 1.5%   Fortunately, at many plants where this could be a problem, the load seldom drops low enough. Or, if the load is de-energized the capacitors are also de-energized. However, if these conditions can't be guaranteed, some or all of the capacitors will have to be switched.

 Additional Notes for Capacitor Compensation at Transformer   Before installing a central PFC system at the transformers, it is advisable to consult the utility company concerned. The modern design of transformer features core laminations that only require a small amount of power for reversal of magnetization. If the capacitor power rating is too high, overvoltage conditions may occur during no-load operation. Capacitors with built-in fuse switch-disconnectors are well suited for direct connection to transformer terminals. In this case, the designer should be aware of the fact that the lines to the capacitor are dimensioned for the full short circuit power. The fuse switches are operated under purely capacitive load. They must therefore never be withdrawn when under load or dangerous arcing may otherwise occur! If it is possible to disconnect the capacitor even when the transformer is switched on, a power capacitor with an automatic circuit breaker must be used. The PFC capacitors can be connected to the secondary side of the transformer in a star or delta connection (see fig.2).   Fig.2

 Calculation of the Capacitor KVAR Rating for Individual Motors

 Induction or "squirrel-cage" motors constitute the single largest group of low power factor loads connected to most power systems making them prime candidates for power factor correction. Fortunately, their reactive power characteristics are nearly constant throughout the entire operating range (Figure 3) making them ideally suited for the application of capacitors. Depending on design, the full load power factor of an induction motor can vary anywhere between 80 to 100 percent, but drops rapidly as the load is decreased (Fig.3). However, when a properly selected capacitor is connected to the motor, the operating power factor of the motor-capacitor combination will remain nearly constant over the entire load range (Fig.3).   Fig.3

 Methods of wiring the Individual power factor correction to Motor Circuits   Figure shows the common connection diagrams for the power factor correction of motors, which are (see Fig.4):   Option#1: On the secondary of the overload relay, Option#2: Between the contactor and the overload relay, Option#3: Between the circuit breaker and the contactor.     Fig.4   For more information about the above common connections, please review Article ”

 Points to Consider When capacitors connected directly across the motor terminals     Two limiting factors must be considered when capacitors are to be switched with a motor as a unit are as follows:   Overvoltage due to self-excitation, Transient torques.   1- Self-excitation voltage:   When a motor is disconnected from the line, it will normally rotate for a short time before coming to rest. A capacitor connected to this motor will still be supplying magnetizing current, which will excite the motor. Under these conditions, the motor and capacitor act like a generator and produce a certain voltage because of this self-excitation. The magnitude of the voltage that can be produced is determined by two things; the rating of the capacitor being used and the speed of the motor involved. It is not uncommon for this .self-excitation voltage to reach 150% of rated voltage if too large a capacitor is being used.   2-Transient torques:   Perhaps even more important than overvoltage is the transient torques that can occur if the motor happens to close back into the line before coming to a complete rest. If the motor is still rotating and acting as a generator, the resulting transient torque may be as much as 20 times the full load torque. Because of transient torque and overload considerations, most motor manufacturers provide recommendations concerning the maximum capacitor KVAR that should be switched with a given motor. These recommendations are conservative enough to avoid endangering the motor, and will ordinarily result in a corrected power factor of approximately 95-98% at full load.   Other important notes:   Certain motor applications are not suitable for connecting the capacitor to the load side of the motor starter. Applications involving reversing, plugging, or frequent starts; crane or elevator motors, or any motor where the load may drive the motor, multispeed motors, or motors using open transition reduced voltage starting, must be corrected on the distribution panel or main service panel. Always choose the capacitor such that the capacitor current is smaller than 90% of the no-load current of the motor (if directly connected). To avoid nuisance blowing of fuses when capacitors are connected directly across the motor terminals: Motors should not be subject to plugging or reversing duty. Motors should not be operated such that rapid restarting occurs

 Methods For Selecting/Calculation The Proper Capacitor KVAR Rating For Motors   There are (5) different methods of selecting/calculation the proper Capacitor KVAR Rating for induction motors. Choose from one of these methods below based on what information you have available. these methods are:   Method#1: Use motor manufacturer’s recommendations Method#2: Use Tables published by leading power factor capacitor manufacturers Method#3: Use NEMA Tables 3, 4, 5 & 6 Method#4: using rule of thumbs Method#5: Using Equations

 Method#1: Use motor manufacturer’s recommendations   Some motors are supplied with maximum KVAR recommendations as in Fig.5     Fig.5

 Method#3: Use NEMA Tables 3, 4, 5 & 6   These Tables lists the recommended sizes of KVAR units needed for correction of most induction motors to approximately 95% power factor. These tables show the proper KVAR for a given horsepower and RPM. For motor types or sizes not listed, please consult the factory.   Table-3   Table-4   Table-5   Table-6

 Method#4: using rule of thumbs   It is widely accepted to use a thumb rule that Motor compensation required in KVAR is equal to:  40% of motor kw-rating or 33% of the Motor Rating in HP.

 Method#5: Using Equations   To calculate required KVAR for energy efficient motors (or any motor) use the following formula:     where:   PF0 Original Power Factor (supplied by manufacturer) PF1 desired Power Factor H.P. Motor Horsepower from nameplate % Motor efficiency from manufacturer nameplate

In the next article, we will explain the Calculation methods of the Capacitor KVAR Rating for buildings and power plants. Please, keep following.

The previous and related articles are listed in below table:

 Subject Of Previous Article Article Glossary of Power Factor Correction Capacitors Types of Loads, The Power Triangle, What is a power factor? Types of power factor Why utilities charge a power factor penalty? Billing Structure What causes low power factor? Bad impacts of low power factor, Benefits of Power Factor correction. How to make Power Factor Correction? Types of Power Factor Correction Capacitors Individual compensation Group compensation, Central compensation, Hybrid compensation. Summary for Power Factor Correction Capacitors Sizing Calculations Steps Step#1: Collect Monthly Billing Data Step#2: Make Some Preliminary Measurements For Current And Voltage Step#3: Fill the Economic Screening Worksheet Step#4: Make Preliminary Measurements For Harmonics Step#5: Repeat the Economic Screening Worksheet Step#6: Compare the Savings with the Probable Cost of Capacitors' Installation Second: Design Phase Step#1: Performing a Detailed Plant Survey Step#1.A: Review the one line diagram Step#1.B: Take into consideration the loads that produce harmonics Step#1.C: collect sufficient data Inventory by using measuring instruments Step#2: Select Economical Capacitor Scheme Step#3: Checking the "No Load" Voltage Rise Step#4: Select Capacitor Switching Options Step#5: Check the Harmonic Distortion and make Harmonic Mitigation Options Step#6: Use the Economic Screening Worksheet again Power Factor Correction Capacitors Sizing Calculations Steps For New Designs

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