Electric power calculations

PHILLIPS ENGINEERS+ CONSULTANTS, INC.
www.phillipsengineers.com
ELECTRIC POWER CALCULATIONS
ROCKY MOUNTAIN
ELECTRICAL LEAGUE
OCTOBER 24, 2002
K. James Phillips, Jr., P.E.
jphillips@phillipsengineers.com

ELECTRIC POWER CALCULATIONS
• OVERVIEW
• PER PHASE
• SHORT CIRCUIT
• PER UNIT
• HARMONICS

WHY ELECTRIC POWER CALCULATIONS
• USED TO PREDICT
OUTCOMES
• SHORT CIRCUITS
• HARMONICS
• VOLTAGES
• LOADS

THE BASICS
• ALL ELECTRICAL THEORY RELATES
BACK TO THE BASICS
• Volts, Amps, Ohms
II
Z
V
V = I * Z
Z = V / I
I = V / Z

SERIES COMBINATIONS
Z1
Z2
Z

COMPLEX IMPEDANCE
R
X
Z
0
X = Z * Sin 0
R = X
X/R
Z = R2+X2

SHORT CIRCUIT REQUIREMENTS
NEC 110-9 AND 110-10
• Articles 110-9 and 110-10
• Equipment shall have adequate
interrupting rating
• Clear faults without extensive damage
• Implies must perform short circuit study

AIC RATINGS
CIRCUIT BREAKER SHORT CIRCUIT
TYPE RATING
QOB 10,000
QOB-H 22,000
QOB-VH 42,000

SHORT CIRCUIT AMPS (SCA)
Source
Circuit Breaker
Source
3 Phase
Circuit Breaker
Line-Ground

PER PHASE ANALYSIS
~
~
~
~
A
B
C A
B
C
Ia
Ib
Ic
~
Three Phase Representation
Single Phase Representation

PER PHASE ANALYSIS EXAMPLE
~
~
~
~
A
B
C A
B
C
Ia
Ib
Ic
~
A 480Y / 277V source is serving a balanced three phase wye resistive load of 20
ohms per phase. What is the current in phase A, B and C?

PER PHASE ANALYSIS
SHORT CIRCUITS
~
~
~
~
A
B
C A
B
C
Ia
Ib
Ic
~

DATA
SOURCE IMPEDANCE
• THEVENIN
EQUIVALANT
IMPEDANCE

DATA
TRANSFORMER IMPEDANCE
• TRANSFORMER
IMPEDANCE

DATA
CONDUCTOR IMPEDANCE
• CONDUCTOR
IMPEDANCE

BASIC SHORT CIRCUIT ANALYSIS
I = V / Z = 277 V / (.001+.01+.085 + 2.0)
I = 277 V / 2.096 ohms
I = 132.156 Amps of load current
I
V
Zsource
.001
Ztransformer
.01
Zconductor
.085
Zload
2.0
277 V

I = V / Z = 277 V / (.001+.01+.085)
I = 277 V / 0.096 ohms
I = 2885.4 Amps of short circuit current
IZsource
.001
Ztransformer
.01
Zconductor
.085
Zload
2.0
Short Circuit
V

SCA < AIC
CALCULATED
SHORT CIRCUIT
AMPS MUST BE
LESS THAN AIC
RATING

CALCULATION TRICK
• VOLTAGE
• %Z
• KVA

CALCULATION TRICK
Transformer
Variable voltage source
Short Circuit
A
Percent Impedance = Percent rated primary
voltage that causes rated base/ambient full
load current to flow in the secondary of a
short circuited transformer.
i.e.. 5.75 percent primary voltage causes
full load current in short circuited secondary,
the percent impedance is 5.75%
%Z = 100%
FLA SCA
SCA = (FLA * 100)
%Z

SHORT CIRCUIT CALCULATION
EXAMPLE:
1500 KVA TRANSFORMER
5.75% IMPEDANCE
480 VOLT SECONDARY
1500 KVA
5.75%
480 VOLTS
SCAMPS?
X

SHORT CIRCUIT CALCULATION
STEP ONE:
FLA = (1500 KVA) / ( .48 KV * SQRT 3 )
FLA = 1804 AMPS
STEP TWO
SCA = (1804 AMPS * 100 ) / 5.75%
SCA = 31,374 AMPS
1500 KVA
5.75%
480 VOLTS
SCAMPS?
X

PROBLEM WITH IMPEDANCE ON TWO
SIDES OF TRANSFORMER
10 : 1 RATIO
X
20 OHMS
0.8 OHMS
Z1(VIEWED FROM SECONDARY)
= Z1 * (1 / 10)2 = 20 Ù * .01 = .002 Ù
Z2(VIEWED FROM SECONDARY)
= Z2 * (10 / 1)2 = 0.8 Ù * 100 = 80 Ù

WHY PER UNIT?
• Calculations that involve impedances at
several voltage levels via transformers,
can become complicated due to the
transformer turns ratio.
• Per unit eliminates need to “reflect”
impedances to different voltages.

PER UNIT EXAMPLE
Example:
A base number of 500 is used. The following is a
summary of per unit values for various numbers:
Number Per Unit Per Cent
250 0.5 p.u. 50%
500 1.0 p.u. 100%
1000 2.0 p.u 200%

BASE QUANTITIES
Current (p.u.) = Actual Current
Base Current
Voltage (p.u.) = Actual Voltage
Base Voltage
Impedance (p.u.) = Actual Impedance
Base Impedance
Power (p.u.) = Actual Power
Base Power

BASE QUANTITIES
• The per unit system requires two base
quantities to be selected:
– Base kVA - Fixed Quantity
– Base Voltage - Variable Based on Voltage
• Two base quantities are calculated:
– Base Impedance - function of base voltage
– Base Current - function of base voltage

BASE KVA
(SELECTED)
BASE KVA (MVA):
In electric power systems, the base quantity that
remains constant throughout the system is the base
kVA. The kVA base is not affected by voltage levels
or transformer turns ratios. The amount of kVA
entering the primary of a transformer is the same as
the kVA leaving the secondary of the transformer
(neglecting transformer losses).
Any arbitrary number may be selected as the kVA
base, however, most electric utilities use a 100,000
kVA base commonly referred to as a 100 MVA base.

BASE VOLTAGE
(SELECTED)
BASE VOLTAGE:
The base voltage will vary depending on the voltage
level of the system. The base voltage is generally
the nominal voltage of a particular voltage level.
PER UNIT VOLTAGE
V p.u. = V actual / V base V actual = V base * V p.u.
Example:
V base = 13.8 kV
V actual = 13.4 kV
V p.u. = 13.4 kV / 13.8 kV = 0.97 p.u.

BASE CURRENT
(CALCULATED)
• I base = MVAbase * 1000 / (sqrt 3 * kVbase)
• I base = kVAbase / (sqrt 3 * kVbase)
PER UNIT CURRENT
I p.u. = I actual / I base I actual = I base * I p.u.
Example:
Bases: 100 MVA, 13.8 kV
I base = (100 MVA * 1000) / (sqrt 3 * 13.8 kV) = 4183 Amps
Actual Amps = 2500 Amps
I p.u. = I actual / I base = 2500 / 4183 = 0.598 p.u.

BASE IMPEDANCE
(CALCULATED)
• Z base = kVbase
2 / MVA base
Per Unit Impedance:
Bases: 100 MVA, 13.8kV
Actual Impedance = 0.32 + j0.27 ohms
Z base = 13.8 kV2 / 100 MVA = 1.90 ohms
Z p.u. = 0.168 + j0.142 p.u.

TABLE OF BASE VALUES
100 MVA - NOMINAL VOLTAGES
Voltage (kV) Impedance
(Ohms)
Current
(Amps)
765 5852.25 75.47
500 2500.00 115.47
345 1190.25 167.35
230 529.00 251.02
138 190.40 418.37
115 132.25 502.04
69 47.61 836.74
34.5 11.90 1673.48
23 5.29 2510.22
13.8 1.90 4183.70

REVIEW
I = V / Z = 277 V / (.001+.01+.085)
I = 277 V / 0.096 ohms
I = 2885.4 Amps of short circuit current
IZsource
.001
Ztransformer
.01
Zconductor
.085
Zload
2.0
Short Circuit
V

SHORT CIRCUIT ANALYSIS
PER UNIT
Zload
V base = 13.8 kV, 3 Phase
MVA base = 100
Assume impedances are all reactive i.e. “X” only. No “R” component.
I = V / Z = 1.0 p.u. / (.002+.03+.098 p.u.)
I = 1.0 p.u. / 0.13 p.u.
I = 7.69 p.u. short circuit current
I base = (MVA base * 1000) / (Sqrt 3 * kV base )
I base = ( 100 MVA * 1000 ) / (Sqrt 3 * 13.8 kV)
I base = 4183.7 Amps
I actual = I p.u. * I base I actual = 7.69 p.u. * 4183.7 Amps I actual = 32,172.6 Amps
IV
Zsource
.002p.u.
Ztransformer
.03p.u.
Zconductor
.098p.u.
1.0 p.u.

HARMONICS
DEFINITION
• Harmonic Order - integer multiple of the
fundamental frequency.
– Harmonic Order Frequency
• 1 ( fundamental) 60Hz
• 2 120Hz
• 3 180Hz
• 4 240Hz
• N N * Fundamental

HARMONICS - 5TH
5th Harmonic (300 Hz)
Fundamental (60 Hz)

NON LINEAR LOAD

SOURCE OF HARMONICS
THE LOAD
• Solid State Motor
Drives
• Rectifiers
• UPS systems
• Computer power
supplies
• Fluorescent lighting
electronic ballast's

FREQUENCY SPECTRUM
1 3 5 7 9 11
Harmonic Order
Magnitude

HARMONIC RELATED PROBLEMS
• Blown Capacitors / Capacitors Fuses
• Transformer Overheating
• Neutral Overheating
• Motor / Generator Overheating
• Equipment Misoperation
• Circuit Breaker Misoperation
• Communication Interference

EFFECTS OF CAPACITORS
• Without capacitors, the
circuit is predominantly
inductive.
• When capacitors are
added, an L-C circuit
results.

SYSTEM IMPEDANCE
INDUCTIVE ONLY
Example:
Power factor correction
requirements dictate that two 600
kvar capacitor banks be installed
at the substation bus. What does
the system impedance look like
before adding capacitors?
Short Circuit
Capacity = 30MVA
Harmonic
Source

SYSTEM IMPEDANCE
INDUCTIVE ONLY
Frequency (harmonic order)
Z
(Ohms
)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Z = jwl, w = 2pi*f, f = frequency

SIMPLIFIED RESONANCE
CALCULATIONS
Example:
Power factor correction
requirements dictate that two 600
kvar capacitor banks be installed
at the substation bus. The utility
short circuit current is 30 MVA
(36,084 Amps @ 480V). What is
the resonance frequency when
the 600 kvar bank is on line and
what is the resonance frequency
when both 600 kvar banks are on
line.
Short Circuit
Capacity = 30MVA
2 x 600 kvar
Capacitor BankHarmonic Source
5TH, 7TH, 11TH, 13TH

CALCULATIONS
MVAsc = short circuit MVA at the capacitor
bank location.
Mvarcap = Mvar rating of the capacitor bank
Source
Impedance
Power
Factor
Capacitor
Harmonic
Source
XL XC
hr = MVAsc = Xc
Mvarcap Xsc

CALCULATIONS
Frequency (harmonic order)
Z
(Ohms
)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1200 kvar 600 kvar
hr = MVAsc =
Mvarcap
30 MVAsc = 7
0.600 Mvarcap
30 MVAsc = 5
1.200 Mvarcap

RESULTS
• PRODUCES SEVERE DISTORTION
• DESIGN CAPACITOR AS HARMONIC
FILTER

IEEE-519
• Sets limits for
voltage and current
distortion at PCC
• PCC is the point of
common coupling

QUESTIONS ???
CONTACT INFORMATION:
PHILLIPS ENGINEERS + CONSULTANTS, INC.
4450 BELDEN VILLAGE ST., N.W. SUITE 309
CANTON, OHIO 44718
Tel: 330.491.0261
Fax: 330.491.0265
jphillips@phillipsengineers.com
DESIGN ENGINEERING
ANALYSIS
FEASABILITY
MANAGEMENT
TRAINING

Electric power calculations

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