Post on 03-Apr-2018
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
http://www.nepsi.com/formulas.htmhttp://www.nepsi.com/formulas.htmhttp://www.nepsi.com/formulas.htm7/28/2019 Useful Formulas for PS Analysis & PF Calculation
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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#A7/28/2019 Useful Formulas for PS Analysis & PF Calculation
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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%20Frequency7/28/2019 Useful Formulas for PS Analysis & PF Calculation
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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.htm7/28/2019 Useful Formulas for PS Analysis & PF Calculation
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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.htm7/28/2019 Useful Formulas for PS Analysis & PF Calculation
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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
7/28/2019 Useful Formulas for PS Analysis & PF Calculation
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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