### Power Factor Correction Capacitors Sizing Calculations – Part Sixteen

In article” Power Factor Correwe indicated that The Main Components of PFC Panel are as follows:

 1- The Main Components of PFC Panel

 A Panel for power factor correction (PFC Panel) is constituted essentially from the following main components: A protective device; A switching device (contactor); One or more capacitors suitably connected; Resistors for capacitor discharge. A PF controller is used In case of an automatic PF compensation system to command switching in/off of the capacitors.

And we explained how to select the first two items (protective devices and contactors) in the past article. Today we will explain the following:

1. How to select a capacitor for PFC Panel and Capacitors’ rules,
2. Capacitor compensation with a detuned reactor,
3. How to Select a Detuned Reactor.

 Third: How To Select A Capacitor For PFC Panel

The capacitor supplies the reactive power necessary to increase the power factor up to the desired value. The characteristics of a capacitor, reported on its nameplate, are:

1- Rated voltage Un;

• According to IEC 60831-1 standard, the rated voltage (UN) of a capacitor is defined as the continuously admissible operating voltage. Capacitors can be selected with their rated voltage corresponding to the network voltage.
• In order to accept system voltage fluctuations, capacitors are designed to sustain over-voltages equal to 1.1 times UN, 8h per 24h. This design margin allows operation on networks including voltage fluctuations and common disturbances.

Note:

• The life expectancy will be reduced if capacitors are used at the maximum level of the working conditions.

2- The rated current (IN):

• The rated current (IN) of a capacitor is the current flowing through the capacitor when the rated voltage (UN) is applied at its terminals, supposing a purely sinusoidal voltage and the exact value of reactive power (KVAR) generated. Capacitor units shall be suitable for continuous operation at an r.m.s. current of (1.3 x IN).

3- Rated frequency f;
4- Reactive power Qc, expressed in KVAR.

Based on operating conditions, Capacitors must be selected according to:

1. Ambient Temperature (°C),
2. Expected over-current, related to voltage disturbances, including maximum sustained over voltage,
3. Maximum number of switching operations/year,
4. Requested life expectancy.
5. Presence of Non-Linear loads: where detuned reactors or filters will be used to mitigate the harmonics effects.

From the data on the nameplate it is possible to obtain the characteristic parameters of the capacitor as follows:

1- For Single-phase circuit

 Rated Current Icn = Qc/Vn Reactance Xc = 1 / w . C Capacitance C = 1 / (w . Xc ) = Qc / 2 . π  . f . Vn2

2- For three-phase circuit

In a three-phase circuit, the capacitors can be star or delta connected; the following table shows the values of power and rated current according to the connection modality.

 Rated current (line) Current in the capacitor banks Power Icn = w . C . Un / √3 Ic = Icn Qc = 3 . Icn. Un = w . C . Un2 Icn = 3 . w . C . Un Ic = w . C .Un Qc = 3 . Icn. Un = 3 . w . C . Un2

 Capacitors’ Selection Rules

 Rule#1: Size of capacitor bank Capacitors are rated in KVAR. Common sizes are 1, 2, 3, 4, 5, 6, 7, 8, 10/12/15/20 and 25 KVAR at 415 or 440V alternating current, 3 phase, 50 Hz. Usually more than one capacitor is required to give the desired degree of power factor correction. Groups of capacitors are factory assembled in various configurations. Standard capacitor ratings are designed for 50 or 60Hz operation. The following equation defines the relation: C= Qc x 109/ (2πfE2) Where: C: capacitance in Farads μF Qc: reactive power in KVAR π =3.1416 f: rated frequency in Hz E: rated voltage in V

 Rule#2: Size of capacitor bank for delta connected 3ph capacitor For delta connected 3ph capacitor, the capacitance value of a capacitor can be calculated using following equation Assuming that capacitance of the three delta connected capacitors are C as shown in the figure. C = Qc × 109 / (4πfE2) Where: C: capacitance in Farads μF Qc : reactive power in KVAR π =3.1416 f: rated frequency in Hz E: rated voltage in V Example#1: 15 kvar, 3 phases, 415V, 50Hz capacitor, calculate its capacitance? Solution: C = Qc × 109 / (4πfE2) C = 15 × 109 / (4 x 3.142 × 50 × (415 × 415)) = 138.62μF

 Rule#3: calculation of capacitor KVAR from measured capacitance For three phase capacitor, KVAR calculation from the measured capacitance value of a capacitor can be done by using the following equation: QM = 2/3 × (Ca + Cb + Cc) × E2 × (2πf)/ 109 Where: QM: capacitor KVAR Ca, Cb & Cc: capacitances measured between phases in μF E: rated voltage in V π =3.1416 f: rated frequency in Hz Example#2: Consider you have measured a capacitor rated for 440volts, 50Hz where in measured capacitance value is as follows: 197μf (between R & Y phase) - Ca 196μf (between B & Y phase) - Cb 200μf (between R & B phase) – Cc Calculate the capacitor KVAR? Solution: QM = 2/3 × (Ca + Cb + Cc) × E2 × (2πf)/ 109 QM = 2/3 ×(197+196+200)×(4402 )×2×3.14×50 / 109 = 24.04 KVAR Note: The tolerance of capacitance of a capacitor is -5% t0 +10% of capacitor as specified in the IEC Standards.

 Rule#4: Calculation Of Rated Current For Capacitor With Rated Supply Voltage And Frequency The following equation will be used: IN = KVAR x 103 / (√3 x UN) Where: IN: Rated current in A UN: rated voltage in V Example#3: For 50 KVAR, 3 phase, 400V, 50Hz capacitor. Calculate the rated current? Solution: IN = KVAR x 103 / (√3 x UN) IN = (50 × 1000) / (1.732 × 400) IN = 72.16 A

 Rule#5: changing the operating voltage It is necessary to note that the reactive power at the service voltage is different from the rated power given on the nameplate and referred to the rated voltage; as a general, if the operating voltage is less than the rated voltage, a reduction in the nameplate KVAR will be realized as follows: Q supplied = Qc (Ue / Un)2 Where: Qc is the reactive power at the rated voltage Un; Q supplied is the effective power at the service voltage Ue. Example#4: A capacitor with 100 KVAR rated reactive power at 500 V, calculate the capacitor KVAR when the applied voltage is 400 V? Solution: Q supplied = Qc (Ue / Un)2 Q supplied = 100 (400/500) 2 = 64 KVAR

 Rule#6: changing the operating voltage and frequency The KVAR of capacitor will not be same if the measured voltage and frequency applied to the capacitor changes, and to calculate capacitor power in KVAR from the measured values at site and name plate data, the following equation will be used: QM = ( fM / fN ) × ( UM / UN )2 × QN Where: QM = Available power in kvar fM = Measured frequency in Hz fN = Rated Frequency in Hz UM = Measured voltage in V UN = Rated Voltage in V QN = Rated power in kvar Example#5: Name plate details: 15kvar, 3 phases, 440V, 50Hz capacitor. Measured voltage 425V and measured frequency - 48.5Hz, calculate the change in capacitor KVAR? Solution: QM = (fM / fN ) × ( UM / UN )2 × QN QM = (48.5/50) × (425 / 440)2 × 15 = 13.57kvar. Also, the current of capacitor will not be same if voltage applied to the capacitor and frequency changes, and to calculate the capacitor current from the measured values at site and name plate data, the following equation will be used: IM = IR (UM x fM) / (UR x FR) Where: IM = Capacitor Current IR = Rated Current UM = Measured Voltage fM = Measured frequency UR = Rated Voltage FR = Rated Frequency Note: Please ensure that the measurement at site is done using true RMS clamp meter. Example#6: Consider a capacitor of 15 KVAR, 440V, 50 Hz, 3 Phase Capacitor Rated Current from name plate 19.68A and Measured Values are: Voltage 425V, Frequency 49.5 Hz, calculate the capacitor current? Solution: IM = IR (UM x fM) / (UR x FR) = 19.68 x(425 x 48.5) / (440 x 50) = 18.43A

 Rule#7: Calculating Capacitor KVAR for three-phase capacitor with filter reactors The following equation will be used: Qc = C.3.V2.2. π.fn / (1-p) Where: Qc: capacitor KVAR C: capacitance in μF V: rated voltage in V π = 3.1412 fn: rated frequency P: blocking factor n: tuning number, n = fr/fn p (as a %): blocking factor; this is the ratio between the reactor inductance XL compared to the capacitor inductance XC. It will be calculated from the following equation: p = XL/XC = 1/n2 = (fn/fr)2 Where: fn: fundamental frequency fr: Harmonic frequency Example#7: For 3 phase capacitor with detuned reactor , the capacitance equal 3 x 332 μF at 400 V /50 Hz with blocking factor p = 7%. Calculate the capacitor KVAR. Solution: Qc = C.3.V2.2. π.fn / (1-p) Qc = 0.000332 x 3 x 400² x 2 x 3.1416 x 50 / (1-0.07) = 53.8 KVAR We can also use the following equation for Calculating effective Capacitor KVAR for three-phase capacitor with filter reactors: Where: Qs: the effective Capacitor KVAR using detuned reactor Us: service voltage Un: nameplate voltage of the capacitor Qn: nameplate KVAR of the capacitor P: blocking factor In this case, using a reactor creates a voltage surge on the terminals of the associated capacitor and the capacitor power supply voltage Uc will be calculated as follows: Uc = Us / (1-p) Note: We should choose a capacitor with nominal voltage Un higher than Uc. Example#8: A capacitor with nominal power of 25 KVAR at 480 V, calculate the effective Capacitor KVAR if a detuned reactor will be used at 400 V. noting that p =14%. Solution: 1- Determine the capacitor power supply voltage: Uc = Us / (1-p)= 400 / (1-0.14) = 465 V 2- Calculate the effective Capacitor KVAR at 400 V:

 Capacitor Compensation With A Detuned Reactor

Functions of Detuned Reactor

On mains supplies with a high level of harmonic pollution, it is recommended to use capacitor banks with detuned reactors which have the following functions:

1. Increasing the capacitor impedance in relation to the harmonic currents,
2. Shifting the parallel resonance frequency of the source and the capacitor to below the main frequencies of the harmonic currents that are causing interference.

The below outline diagram represents an electrical installation with capacitor bank, reactor impedance and a load that generates harmonics, the detuned reactors function will change according to the frequency as follows:

1. The detuned reactor and capacitor assembly is capacitive for frequencies below fr, so allows reactive energy compensation.
2. The detuned reactor and capacitor assembly is inductive, so prevents amplification of the harmonics.

Note:
The serial frequency (fr) chosen must be below the first harmonic order present in the circuit.

The most commonly used reactor tuning frequencies are:

 Tuning frequency (Hz) * Blocking factor (P %) Tuning number (n) 215 5.4 4.3 189 7 3.78 135 14 2.7

*With network frequency 50 Hz,

Where:

n: tuning number, n = fr/fn
p (as a %): blocking factor; this is the ratio between the reactor inductance XL compared to the capacitor inductance XC. It will be calculated from the following equation:

p = XL/XC = 1/n2 = (fn/fr)2

Where:

fn: fundamental frequency
fr: Harmonic frequency

 When/How to Use Detuned Reactor To use a detuned reactor, you need to make a correct assessment of the risks of capacitor bank resonance in your installation, we recommend the following procedure: Take measurements over a significant period (minimum one week) of the voltages, currents, power factor, level of harmonics (individual and global THD-U/THD-I). Size the capacitor bank appropriately for its reactive energy compensation requirements, based on these measurements and your electricity bills. For each step power rating (physical or electrical) to be provided in the capacitor bank, calculate the resonance harmonic orders: where S is the short-circuit power at the capacitor bank connection point, and Q is the power rating for the step concerned. If one of the calculated harmonic orders corresponds to one of the harmonics in the installation (with accuracy of ±10 %), it may be necessary to use detuned reactors in order to shift the resonance to a harmless frequency range.

 How to Select a Detuned Reactor

 First: For 3 Phase Capacitors The reactor value (inductance per phase) L is calculated from the following equation: Where: L: The reactor value (inductance per phase) in Henry H Us: service voltage P: blocking factor Qs: the effective Capacitor KVAR using detuned reactor Un: nameplate voltage of the capacitor Qn: nameplate KVAR of the capacitor ω=2πf And the current IL in the reactor will be calculated from the following equation: IL = Qs / √3 Us Example#9: Use the same data from Example#8; calculate the reactor inductance value (per phase) and the reactor current. Solution: 1- the reactor inductance value (per phase) 2- the reactor current IL = Qs / √3 Us = 20000 / √3 x 400 = 28.9 A

 Second: For 3 Single Phase Capacitors The reactor value (inductance per phase) L is calculated from the following equation: Where: L: The reactor value (inductance per phase) in Henry H Us: service voltage P: blocking factor Qs: the effective Capacitor KVAR using detuned reactor Un: nameplate voltage of the capacitor Qn: nameplate KVAR of the capacitor ω=2πf And the current IL in the reactor will be calculated from the following equation: IL = Qs / 3 Us Example#10: A capacitor with nominal power of 25 KVAR at 480 V, calculate the effective Capacitor KVAR if a detuned reactor will be used at 400 V. noting that p =14%. Solution: 1- The reactor inductance value (per phase) 2- The reactor current IL = Qs / √3 Us = 20000 / 3 x 400 = 16.6 A

In the next article, we will explain how to choose Resistors, PF Controllers and Cables for Power Factor Correction Capacitors Calculators. 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 Factors Affecting The Rated KVAR For a Capacitor Calculation of the Capacitor KVAR Rating for Compensation at: 1-Transformer 2-Individual Motors 3- Calculation Of The Capacitor KVAR Rating For Buildings And Power Plants(Group Compensation) Harmonics Effects On Power Factor Capacitors Harmonic Limits in Electric Power Systems (IEEE 519-2014) Options to Reduce Harmonics for PFCC Power Factor Compensation In Case Of Harmonics Power Factor Correction Capacitors Calculators: 1- Arteche Reactive Power and Harmonic Resonance Point Calculator, 2- Eaton Power Factor Correction Calculator, 3- AccuSine Sizing Spreadsheet, 4- Square-D (Schneider Electric) Calculator. The Main Components of PFC Panel How to select Circuit Breakers for PFC Panel How to select Fuses for PFC Panel How to select Contactors for PFC Panel

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