Useful Formulas for PS Analysis & PF Calculation

7/28/2019 Useful Formulas for PS Analysis & PF Calculation

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Useful Formulas for Power System Analysis

& Power Factor Correction

The formulas on this web page may be utilized in designing power factor correction systems

and harmonic filter banks.

Programs

Harmonic Analysis Program

Formula Symbols

C Capacitance (farads)fs System Frequency

f Frequency (Hertz)

I Current (amps)

I1, I2 Currents of bank or stages being switched and of bank or stage already energized

Imax peak A peak value calculated without damping. In practical circuits it will be about 90 percent of thisvalue

Ih RMS current (amps) at harmonic (h)

Kvar Reactive Power (kvar)

kVAtx Three-phase transformer ratingZtx Nameplate impedance (%)

kVAr Three-phase capacitor bank rating

KVA Total Power (kVA)

kV kilovolts (kv)

KW Real Power (kw)

Leq Total equivalent inductance per phase between capacitor banks or stages, in

microhenrys

PF Power Factor (no unit)

P Real Power (KW)

Q Reactive Power (kvar)

S Total Power (KVA)

Subscript I Initial

Subscript d Desired

Subscript Three Phase
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Subscript Single Phase

Subscript LN Line to Neutral

Subscript LL Line to Line

Subscript SC Short Circuit

Th Single Frequency TIF at harmonic (h)

Vn Harmonic Voltage magnitude

Vrms Root mean square (rms) value of voltage

VLL Rated maximum voltage in kilovolts

I rms Root mean square (rms) value of current

Isc

Symmetrical rms short-circuit current, in amperes

VpkPeak magnitude

Xc Capacitive Reactance (ohms)

XC Capacitive reactance ()

XL Inductive reactance ()

R Resistance ()

Xn Filter inductor - reactance ()

n Harmonic at which filter is tuned

Power factor angle

Formula Index

A) Capacitors Connected in Parallel

B) Capacitors Connected in Series

C) Capacitive Reactance

D) Capacitance

E) Capacitor KilovarsF) Power Factor

G) Kilovars Required to Change Power Factor

H) Equations for Total Power FactorI) Total Power

J) Reactive Power

K) Voltage Rise

L) Released System Capacity for Power Factor ImprovementM) Loss Reduction for Correcting Power Factor

N) Capacitor Current

O) Total Harmonic DistortionP) Root Mean Square, RMS

Q) Displacement Power Factor, DPF

R) Total Power Factor, TPF

S) Resonant Frequency, h
http://www.nepsi.com/formulas.htm#Ahttp://www.nepsi.com/formulas.htm#Ahttp://www.nepsi.com/formulas.htm#B%29%20Capacitors%20Connected%20in%20Serieshttp://www.nepsi.com/formulas.htm#B%29%20Capacitors%20Connected%20in%20Serieshttp://www.nepsi.com/formulas.htm#C%29%20Capacitive%20Reactance%20Xchttp://www.nepsi.com/formulas.htm#C%29%20Capacitive%20Reactance%20Xchttp://www.nepsi.com/formulas.htm#D%29%20Capacitance%20Chttp://www.nepsi.com/formulas.htm#D%29%20Capacitance%20Chttp://www.nepsi.com/formulas.htm#E%29%20Capacitive%20Kilovarshttp://www.nepsi.com/formulas.htm#E%29%20Capacitive%20Kilovarshttp://www.nepsi.com/formulas.htm#F%29%20Power%20Factorhttp://www.nepsi.com/formulas.htm#F%29%20Power%20Factorhttp://www.nepsi.com/formulas.htm#G%29%20Kvars%20required%20to%20change%20power%20factorhttp://www.nepsi.com/formulas.htm#G%29%20Kvars%20required%20to%20change%20power%20factorhttp://www.nepsi.com/formulas.htm#Hhttp://www.nepsi.com/formulas.htm#Hhttp://www.nepsi.com/formulas.htm#Ihttp://www.nepsi.com/formulas.htm#Ihttp://www.nepsi.com/formulas.htm#J%29%20Equations%20For%20Reactive%20Powerhttp://www.nepsi.com/formulas.htm#J%29%20Equations%20For%20Reactive%20Powerhttp://www.nepsi.com/formulas.htm#Khttp://www.nepsi.com/formulas.htm#Khttp://www.nepsi.com/formulas.htm#K%29%20Released%20System%20Capacity%20for%20power%20factor%20improvementhttp://www.nepsi.com/formulas.htm#K%29%20Released%20System%20Capacity%20for%20power%20factor%20improvementhttp://www.nepsi.com/formulas.htm#L%29%20%25%20Loss%20Reduction%20for%20correcting%20power%20factorhttp://www.nepsi.com/formulas.htm#L%29%20%25%20Loss%20Reduction%20for%20correcting%20power%20factorhttp://www.nepsi.com/formulas.htm#nhttp://www.nepsi.com/formulas.htm#nhttp://www.nepsi.com/formulas.htm#O%29%20Total%20Harmonic%20Distortionhttp://www.nepsi.com/formulas.htm#O%29%20Total%20Harmonic%20Distortionhttp://www.nepsi.com/formulas.htm#P%29%20Root%20Mean%20Square,%20RMShttp://www.nepsi.com/formulas.htm#P%29%20Root%20Mean%20Square,%20RMShttp://www.nepsi.com/formulas.htm#Q%29%20Displacement%20Power%20Factorhttp://www.nepsi.com/formulas.htm#Q%29%20Displacement%20Power%20Factorhttp://www.nepsi.com/formulas.htm#R%29%20Total%20Power%20Factor,%20TPFhttp://www.nepsi.com/formulas.htm#R%29%20Total%20Power%20Factor,%20TPFhttp://www.nepsi.com/formulas.htm#S%29%20Resonant%20Frequencyhttp://www.nepsi.com/formulas.htm#S%29%20Resonant%20Frequencyhttp://www.nepsi.com/formulas.htm#S%29%20Resonant%20Frequencyhttp://www.nepsi.com/formulas.htm#R%29%20Total%20Power%20Factor,%20TPFhttp://www.nepsi.com/formulas.htm#Q%29%20Displacement%20Power%20Factorhttp://www.nepsi.com/formulas.htm#P%29%20Root%20Mean%20Square,%20RMShttp://www.nepsi.com/formulas.htm#O%29%20Total%20Harmonic%20Distortionhttp://www.nepsi.com/formulas.htm#nhttp://www.nepsi.com/formulas.htm#L%29%20%25%20Loss%20Reduction%20for%20correcting%20power%20factorhttp://www.nepsi.com/formulas.htm#K%29%20Released%20System%20Capacity%20for%20power%20factor%20improvementhttp://www.nepsi.com/formulas.htm#Khttp://www.nepsi.com/formulas.htm#J%29%20Equations%20For%20Reactive%20Powerhttp://www.nepsi.com/formulas.htm#Ihttp://www.nepsi.com/formulas.htm#Hhttp://www.nepsi.com/formulas.htm#G%29%20Kvars%20required%20to%20change%20power%20factorhttp://www.nepsi.com/formulas.htm#F%29%20Power%20Factorhttp://www.nepsi.com/formulas.htm#E%29%20Capacitive%20Kilovarshttp://www.nepsi.com/formulas.htm#D%29%20Capacitance%20Chttp://www.nepsi.com/formulas.htm#C%29%20Capacitive%20Reactance%20Xchttp://www.nepsi.com/formulas.htm#B%29%20Capacitors%20Connected%20in%20Serieshttp://www.nepsi.com/formulas.htm#A


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T) I*T Product

U) Quality Factor, Q

V) Crest Factor, CF

W) Inrush Current Calculation for Single Capacitor Bank SwitchingX) Inrush Current Calculation for Back-To-Back Capacitor Bank Switching

Formulas

A) Capacitors Connected in Parallel

B) Capacitors Connected in Series

C) Capacitive Reactance Xc
http://www.nepsi.com/formulas.htm#S%29%20Resonant%20Frequencyhttp://www.nepsi.com/formulas.htm#S%29%20Resonant%20Frequencyhttp://www.nepsi.com/formulas.htm#U%29%20Quality%20Factor,%20Qhttp://www.nepsi.com/formulas.htm#U%29%20Quality%20Factor,%20Qhttp://www.nepsi.com/formulas.htm#V%29%20Crest%20Factor,%20CFhttp://www.nepsi.com/formulas.htm#V%29%20Crest%20Factor,%20CFhttp://www.nepsi.com/capacitivereactance.htmhttp://www.nepsi.com/cap_series.htmhttp://www.nepsi.com/cap_parallel.htmhttp://www.nepsi.com/capacitivereactance.htmhttp://www.nepsi.com/cap_series.htmhttp://www.nepsi.com/cap_parallel.htmhttp://www.nepsi.com/capacitivereactance.htmhttp://www.nepsi.com/cap_series.htmhttp://www.nepsi.com/cap_parallel.htmhttp://www.nepsi.com/capacitivereactance.htmhttp://www.nepsi.com/cap_series.htmhttp://www.nepsi.com/cap_parallel.htmhttp://www.nepsi.com/capacitivereactance.htmhttp://www.nepsi.com/cap_series.htmhttp://www.nepsi.com/cap_parallel.htmhttp://www.nepsi.com/capacitivereactance.htmhttp://www.nepsi.com/cap_series.htmhttp://www.nepsi.com/cap_parallel.htmhttp://www.nepsi.com/formulas.htm#V%29%20Crest%20Factor,%20CFhttp://www.nepsi.com/formulas.htm#U%29%20Quality%20Factor,%20Qhttp://www.nepsi.com/formulas.htm#S%29%20Resonant%20Frequency


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D) Capacitance C

E) Capacitive Kilovars

F) Power Factor

G) Kvars Required to Change Power Factor

where:

= Initial Power Factor Angle

= Final Power Factor Angle
http://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htmhttp://www.nepsi.com/kvars_required_calculation.htmhttp://www.nepsi.com/power_factor_calculation.htmhttp://www.nepsi.com/kvar_calculation.htmhttp://www.nepsi.com/cap_calculation.htm


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H) Equations for Total Power

good for both 3 phase andsingle phase calculations

I) Total Power

J) Equations For Reactive Power

K) Approximate Voltage Rise for Addition of Capacitors

where:
http://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htmhttp://www.nepsi.com/voltagerise.htmhttp://www.nepsi.com/real_power_calculation.htmhttp://www.nepsi.com/reactive_power_calculation.htmhttp://www.nepsi.com/total_power_calculation.htm


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L) Released System Capacity for Power Factor Improvement

M) % Loss Reduction for Correcting Power Factor

N) Capacitor Current

O) Total Harmonic Distortion

P) Root Mean Square, RMS

Q) Displacement Power Factor

R) Total Power Factor, TPF

S) Resonant Frequency


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T) I*T Product

U) Quality Factor, Q

V) Crest Factor, CF

W) Inrush Current and Frequency Calculation for Single Capacitor Bank Switching

X) Inrush Current and Frequency Calculation for Back-To-Back Capacitor Bank

Switching

Useful Formulas for PS Analysis & PF Calculation

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