tab 18 - apparent power, active power, reactive...

© 2012, Siemens Industry Inc., all rights reserved

Tab 18 -

Apparent Power, Active Power, Reactive Power Distribution Systems Engineering -

Course 1

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15-2Siemens Industry

Inc., Siemens Power Technologies International

Some Basic Concepts

Review of some important definitions:

Peak Value of a sinusoidal current wave (Ipeak

)•

Occurs when the sinusoidal current wave is at its maximum amplitude

RMS Value (also called effective value) of a sinusoidal current wave

Average Value of a sinusoidal current wave

02sin10

T

peakaverage dttTI

TI

peakpeakT

peakRMS II

dttT

IT

I 707.02

2sin10

22

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Voltage and current relationship

)90sin(sin2)sin(cos2)sin(2)sin()( oRMSRMSRMSMAX tItItItIti

)sin(2)sin()( tVtVtv RMSMAX

)sin(cos2)( tIti RMSR

v(t)

i(t) LOADiR(t) iX(t)

• COMPONENTS OF TOTAL CURRENT

• TOTAL CURRENT

)90sin(sin2)( oRMSX tIti

• SYSTEM VOLTAGE v(t)

• COMPONENT OF CURRENT IN-PHASE WITH VOLTAGE (REAL COMPONENT)Real component of current supplies a NET energy to the LOAD

• COMPONENT OF CURRENT 90O

OUT-OF-PHASE WITH VOLTAGE (IMAGINARY COMPONENT)Imaginary component of current supplies no NET energy to the load

θ

= Angle by which voltage v(t) leads total current i(t)

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Voltage and current relationship (continued)

)90sin(sin2)sin(cos2)sin(2)( oRMSRMSRMS tItItIti

)sin(cos2)( tIti RMSR

v(t)

i(t) LOADiR(t) iX(t)

• TOTAL CURRENT

)90sin(sin2)( oRMSX tIti

• REAL COMPONENT OF CURRENT • IMAGINARY COMPONENT OF CURRENT

• RMS VALUE (IR

) OF REAL COMPONENT OF CURRENT:

• RMS VALUE (IX

) OF IMAGINARY COMPONENT OF CURRENT:

cosRMSR II

sinRMSX II

• RMS VALUE (IRMS

) OF TOTAL CURRENT: 22 XRRMSTOTAL IIII

IR

IX

ITOTAL

RELATIONSHIP BETWEEN RMS VALUE OF REAL COMPONENT, IMAGINARY COMPONENT, AND TOTAL CURRENT WHEN ANGLEΘ

IS POSITIVE:

θ

= Angle by which voltage v(t) leads current i(t)

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Voltage, current, & power relationship

)sin()()sin()( tItiandtVtv MAXMAX

)sin()sin()()()( ttIVtitvtp MAXMAX

)2sin(sin22

)2cos(1cos22

)( tIVtIVtp MAXMAXMAXMAX

• INSTANTANEOUS AND AVERAGE POWER

• USING TRIGONOMETRIC IDENTITIES, THE EXPRESSION FOR INSTANTANEOUS POWER p(t) IS:

)2sin(sin)2cos(1cos)( tIVtIVtp RMSRMSRMSRMS

• INSTANTANEOUS POWER, p(t), IS THE RATE AT WHICH ENERGY IS SUPPLIED TO THE LOAD

“+”

p(t) means system supplies energy to load, “-”

p(t) means load supplies energy back to system. Frequency of p(t) is twice that of system

Note that the real component of current, IRMS cosθ, produces one component of the instantaneous power thathas a non-zero average value. The imaginary component of current, IRMS sinθ, produces the second componentof instantaneous power that has an average value of zero.

v(t)

i(t)

LOAD

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Voltage, current, & power relationship (continued)

)2sin(sin)2cos(1cos)( tIVtIVtp RMSRMSRMSRMS

)2sin()2sin(sin)( tQtIVtp RMSRMSQ )2cos(1)2cos(1cos)( tPtIVtp RMSRMSP

• EXPRESSION FOR INSTANTANEOUS POWER

• THE INSTANTANEOUS POWER CAN ARBITRARILY BE SPLIT INTO TWO COMPONENTS CALLED pP

(t) AND pQ

(t)

(ACTIVE

AND REACTIVE

POWER RESPECTIVELY)

ACTIVE POWER , pp

(t) REACTIVE POWER , pQ

(t)

WattsinIVdttpT

P RMSRMST

AV cos)(1

0

• AVERAGE POWER SUPPLIED TO THE LOAD OVER INTEGER MULTIPLES OF PERIOD T IS:

• AVERAGE VALUE OF ACTIVE POWER = P • PEAK VALUE OF REACTIVE POWER = QcosRMSRMS IVP sinRMSRMS IVQ

• THE APPARENT POWER

IN THE CIRCUIT, S, IS THE PRODUCT OF THE RMS VALUE OF THE VOLTAGE,VRMS

,

AND THE RMS VALUE OF THE CURRENT, IRMS

:

RMSRMS IVS

22 QPS P

QS

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15-7Siemens Industry Inc., Siemens Power Technologies International

Voltage, current, & power relationship (continued)

•

EXAMPLE CALCULATION 1A SINGLE-PHASE TWO WIRE CIRCUIT OPERATES AT 7620 VOLTS RMS BETWEEN THE TWO WIRES.THE CURRENT IN THE PHASE WIRE IS MEASURED AT 25 AMPERES RMS. A METER CONNECTEDTO THE CIRCUIT SHOWS THE ACTIVE (REAL) POWER SUPPLIED IS 150 KW

1.

WHAT IS THE APPARENT

POWER SUPPLIED BY THE CIRCUIT?2.

WHAT IS THE REACTIVE

POWER SUPPLIED BY THE CIRCUIT?

LOADVRMS = 7620 VOLTS

IRMS = 25 AMPS

kVAAMPERESVOLTIVS RMSRMS 5.190500,19025*7620.1 kWPGIVEN 150:

kVArQPSQorQPS 43.1171505.190,,.2 222222

IF THE LOAD WERE MODIFIED IN SOME MANNER SUCH THAT IT DRAWS ONLY

150 kW OF REAL POWER (P) AND NO REACTIVE POWER (Q = 0), WHAT WOULD THE LINE CURRENT BE IN

AMPERES?

RMSRMS IVPSQWITHTHEN :0

AMPERESV

PIRMS

RMS 69.19620,7000,150

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Apparent Power (complex number)

The combination of active and reactive power is referred to as apparent power, defined as follows with complex number notation:

S

= P

+ jQS

= VI

cos

+ j VI

sin

whereS is the apparent power (VA)P is the active power (W)Q is the reactive power (VAR)θ

is the angle between the voltage and the current (voltageangle –

current angle in this definition)P is related to energy that becomes heat, light, mechanical motion,etc.Q is related to energy that is stored in an inductor in ½

cycle, and then returned to the system in the next ½

cycle.

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Apparent Power Equations

• APPARENT POWER “S”

IN TERMS OF VOLTAGE (V) AND CURRENT (I) AS COMPLEX NUMBERS

XRXR VjVVandVjVV *

XRXR IjIIandIjII *

XjRZ

V = VOLTAGE PHASOR (A COMPLEX NUMBER) –

RMS VALUEVR

= REAL

PART OF VOLTAGE PHASOR V –

RMS VALUEVX

= IMAGINARY

PART OF VOLTAGE PHASOR –

RMS VALUEV*

= COMPLEX CONJUGATE OF V

I = CURRENT PHASOR (A COMPLEX NUMBER) –

RMS IR

= REAL

PART OF CURRENT PHASOR I –

RMSIX

= IMAGINARY

PART OF CURRENT PHASOR I –

RMSI*

= COMPLEX CONJUGATE OF I -

RMS

*

2

*

***

ZV

ZVV

ZVVIVjQPS

ZIZIIIZIIVjQPS

2***

XRRXXXRRXRXR IVIVjIVIVIjIVjVIVQjPS *

XXRR IVIVP XRRX IVIVQ

• APPARENT POWER S

•

ACTIVE (REAL) POWER

• REACTIVE (IMAGINARY) POWER

V VX

VR

I

IXIR

ZV0o

I

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Apparent Power Equations (continued)

• EXAMPLE CALCULATION 2

THE OUTPUT OF A COMPUTER PROGRAM GIVES THE FOLLOWING FOR THE VOLTAGE AND CURRENTIN A SINGLE-PHASE LINE (SEE GENERALIZED SKETCH ABOVE)

VOLTAGE “V”

IS 7620 VOLTS AT AN ANGLE OF 10 DEGREESLINE CURRENT “I”

IS 25 AMPERES AT AN ANGLE OF -28.057 DEGREESWHAT IS THE ACTIVE (REAL) POWER AND REACTIVE (IMAGINARY) POWER SUPPLIED TO THE LOAD?

WATTSIVIVP XXRR 1.998,149759.11*20.1323062.22*24.7504 VARSIVIVQ XRRX 434,117)759.11(*24.7504062.22*20.1323

• REAL AND IMAGINARY PART OF VOLTAGE PHASOR:

VoltsVandVoltsV oXo

R 20.1323)0.10(sin762024.7504)0.10(cos7620

AmpsIandAmpsI oXo

R 759.11)057.28(sin0.25062.22)057.28(cos0.25

• REAL AND IMAGINARY PART OF LINE CURRENT PHASOR:

• ACTIVE (REAL) AND REACTIVE (IMAGINARY) POWER TO LOAD

Note: The V, I, P, and Q values in this example are the same as

in example calculation 1

V VX

VR

I

IX

IRZV 0o

I

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Apparent Power Equations (continued)

cosRMSRMS IVP

• EXAMPLE CALCULATION 2 (continued)

The active and reactive power, for this example, also can be calculated with the relationships below.

sinRMSRMS IVQ

θ

= Angle by which voltage v(t) leads current i(t)

VoltsVRMS 7620 AmperesIRMS 25

0057.38)057.28(0.10 ooIV

kWWattsP o 0.1503.999,149)057.38cos(25*7620

kVArVarsQ o 43.1178.432,117)057.38sin(25*7620

GIVENS:

θV

= VOLTAGE ANGLE

θI

= CURRENT ANGLE

ACTIVE (REAL) POWER:

REACTIVE (IMAGINARY) POWER:


The Power Triangle Revisited

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Phasor Diagram of the Power Triangle

kVAkVAR

kWO

O

kVAkVAR

kW

INDUCTIVE LOAD CAPACITIVE LOAD

POWER FACTOR IS THE COSINE OF THE ANGLE BETWEEN THE APPARENT POWER

(kVA)

ANDTHE ACTIVE POWER (kW).

FOR INDUCTIVE LOAD THE REACTIVE POWER (VARS) IS “+”

IN SIGN

FOR CAPACITIVE LOAD THE REACTIVE POWER (VARS) IS “-”

IN SIGN

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Power Equations Revisited (Again!)

kVAkVAR

kWO

INDUCTIVE LOAD

• RELATIONSHIPS BETWEEN POWER FACTOR AND REACTIVE FACTOR:

sinkVAkVAR

coskVAkW

22 kVARkWkVA

kVAkVARFACTORREACTIVERF

kVAkWFACTORPOWERPF

220.1 RFPF

• RELATIONSHIPS BETWEEN KVA, KW, AND KVAR:


Energy –

Billing and Load Composition

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Customers and Loads

As engineers we think of the customers as electrical loads that the power delivery system is designed to serve

Generation

Transmission

Primary Distribution

Secondary Distribution

The accountants see the electrical loads as customers (sources of revenue)

The customer has a meter that measures what they use, and the Utility sends them monthly bills that recover the cost of supplying the power

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The kWh Meter –

Residential Customers

An electro-mechanical type of kilowatt-hour meter to measure energy consumption

Flux from current and voltage coils interact producing a torque on the disc. The rotational speed of the disk is proportional to the real power (kW). Time integration of the power thru a gear mechanism is the energy consumed, as displayed on the dials.

A kWh meter only measures the active power. The amount of reactive power consumed (VARs) are not measured.

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The kVA Meter –

Industrial and Commercial Customers

Used to meter commercial and industrial loads

Monitors the kW and kVAR as well as the usage in time periods.

Digital readouts

Meter data can be downloaded to hand held computer

Meter can be read remotely

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What Are Electrical Loads?

The electric power system elements have both a resistive and reactive component

Resistive Components (R)•

Overhead line & Underground cable circuit conductor resistance•

Transformer winding resistance

Reactive Components (XL

, XC

)•

Overhead line & Underground cable circuit reactance•

Transformer winding leakage reactance•

Phase reactor reactance for limiting short circuit current •

Series capacitors to cancel line inductive reactance

Loads are comprised of

Resistive elements •

I2

* R = kW

Reactive elements•

I2

* X = kVAR

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Load Composition

Constant Power Loads•

Demand the same amount of kVA

regardless of the voltage supplied to them

Constant Current Loads•

Demand the same current regardless of the voltage applied

Constant Impedance Loads•

At all times, present the same impedance to the system, irrespective of voltage applied to them

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Load Categories

Residential

Single and multiple phases; seasonal

Commercial

Light to heavy

Industrial

Light to heavy with multiple shifts

Agricultural

Short burst of high demand

Lighting

Changes with time of year

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Distribution Circuits

They are an aggregate of the different types of loads categories

The demands fluctuate

The power factor for each load type is not the same

Each load has a different requirement with respect to the quality of power supply


Tab 19 -

Power Quality Overview Distribution Systems Engineering –

Course 1

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Siemens Energy Inc., Power Technologies International 16-2

What is power quality?

Voltage disturbances related to power quality

Causes of PQ problems

Power quality standards

Solutions

Topics

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Siemens Energy

Inc., Power Technologies International 16-3

What Is Good Power Quality?

Utility perspective:

The relative absence of utility-caused voltage variations at the point of common coupling (PCC).

Customer perspective:

Electric power which supports their operations with minimal power induced equipment disturbances and failures.

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Siemens Energy


Ideal Voltage Conditions

Voltage magnitude is well within ANSI C84.1 Range A (normal operation) limits

Sags, swells, or transient voltages are non-existent or very minor

No momentary or permanent interruptions (outages)

Harmonic distortion and noise are well within specified limits

No observable flicker

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Siemens Energy


Power Quality Disturbances

Long duration voltage variations

steady-state overvoltages

& undervoltages

sustained interruptions (permanent faults)

Short duration voltage variations

momentary interruptions (clearing temporary faults and reclosing)

sags & swells (from faults on system)

Frequency variations

Transients

impulsive

oscillatory

Voltage unbalance (imbalance)

Voltage fluctuations

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Siemens Energy


Power Quality Disturbances (continued)

Waveform distortion

harmonics & interharmonics

noise

notching

Reliability issues

momentary outages (interruptions)

permanent outages (interruptions)

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Siemens Energy


VOLTAGE SAGS ARE THE MOST COMMON POWER QUALITY DISTURBANCE EXPERIENCED BY END USERS

ITIC CURVE PROVIDES GUIDANCE TO EQUIPMENT MANUFACTURERS ON VOLTAGE SUSCEPTIBILITY THAT THEY SHOULD DESIGN INTO THEIR EQUIPMENT

POINTS ON ITIC CURVE ARE AN AGGREGATION OF OVER 3000 VOLTAGE EVENTS RECORDED AT 100 LARGE MANUFACTURING PLANTS IN THE USA OVER A PERIOD OF ONE YEAR

Power Quality Disturbances (continued) Voltage Sags

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Siemens Energy


Substation Bus Voltage Sag for SLG Fault on Radial Feeder

32" 32"

48"

Oa Oc

Ob

n

DISC: CE Dist Course, 2006, #1Con Ed OH Line Z1 Z0.FCW

R1 = 0.198 Ohms / mileX 1 = 0.583 Ohms / mile

R0 = 0.485 Ohms / mileX 0 = 1.901 Ohms / mile

477 MCM AL PHASE4/0 CU NEUTRAL

• FACTORS WITH SIGNIFICANT IMPACT ON SUBSTATION BUS VOLTAGE

1.

AVAILABLE 3-PHASE AND SLG FAULT CURRENT ON SUB BUS (Z0

& Z1

)

2.

IMPEDANCE OF FAULTED FEEDER IN OHMS PER UNIT LENGTH

3.

DISTANCE FROM SUBSTATION TO FAULT (L)

LINE CONFIGURATIONAND IMPEDANCES

FOR PLOTS

SUB 13.2 KVBUS

FAULTED FEEDER (SLG PHASE A)

L

UNFAULTED FEEDERS

Z0Z1

Disk: CE Dist Course 2006, #1Sub Bus V, SLG FLT.FCW

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Substation Bus Voltage Sag for SLG Fault on Radial Feeder (continued)

• SUBSTATION LINE-TO-GROUND BUS VOLTAGES –

13.2 kV SYSTEMFEEDER FAULTED PHASE = A, UNFAULTED PHASES = B & C

Notes:Substation bus sag andswell applied to all unfaulted

feeders untilfaulted feeder breakeropens.

For selected configuration, unfaulted

phase C bus voltage swell is less than unfaulted

phase B bus voltage swell.

In 27 kV system, voltage sag on substation bus (with same available fault current as at 13.2 kV), will be greater than sag at 13.2 kV.

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Power Quality Disturbances (continued)

• EXAMPLE OF CONDITION CREATING VOLTAGE UNBALANCE FORSMALL THREE-PHASE PUMPING APPLICATION

FLOATING-WYE DELTA TRANSFORMER BANK FOR 4-WIRE DELTA SERVICE

POWER LEG TRANSFORMERS = 10 KVA

LIGHTING LEG TRANSFORMER = 15 KVA

OPEN FUSE CUTOUTON ONE OF THE POWERLEG TRANSFORMER

4-WIRE DELTA SERVICE SUPPLYING A 3-PHASE PUMPING APPLICATION

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Then Versus Now

Power quality today is not the same as power quality in 1950

With the increase in nonlinear devices, the power has become ’dirty’

with lots of voltage and current distortion

It can present a localized problem that results in overheating of transformers and fuses due mainly to the presence of high harmonic currents

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Customers -

Sensitive Equipment

Industrial equipment failures (Power supplies & motors)

One study suggests that current surges following a voltage sag is more responsible for failures than are surge overvoltages

Industrial/commercial concerns

computer drive manufacturing systems

PCs for data processing and management application

adjustable speed drives/motor driven assembly systems

Programmable logic controllers (PLC)

Computer numerical control (CNC) machines

Servo Drives

Robots

the increasingly competitive nature of manufacturing

the effect of non-linear loads on utility system, other customers and plant equipment

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Customers -

Sensitive Equipment (continued)

Residential concerns

VCRs

digital clocks

home PCs

various other sags and outage sensitive electronic devices

Residential concern, open neutral in 120/240-volt service

Causes steady state overvoltages

/undervoltages

Disk: CE Dist Course 2006, #1Open Neutral Secondary.FCW

X1

X3

X2

H1

H2

120 V LOAD

120 V LOAD240 V LOAD

DISTRIBUTIONTRANSFORMER

O

OPENNEUTRAL

RESISTANCE TO GROUND AT SERVICE (ROD, H20 PIPE)

120 V

120 V

1

O2

V1

V2

HV O

POLE GROUNDCONNECTION

1-PHASE 3-WIRE SERVICE 3-WIRE LOAD

PN

SN

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Origins of Power Quality Problems

Utility problems

weak system (High Impedance with load injecting high harmonic currents)

single phasing in three-phase lines

open neutral on primary or secondary system

poor system design

fault induced momentary outages, voltage sags and voltage swells

equipment failures (transformers, splices, etc)

switching surges

capacitor switching transients

lightning surges

harmonic resonance

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Origins of Power Quality Problems (continued)

Customer caused problems

poor system design or defective wiring

interaction of loads

grounding problems and loops

electromagnetic compatibility problems

Harmonics

switching of large loads (e.g. motors, arc furnaces) producing flicker

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Origins of Power Quality Problems (continued)

Manufacturers of Utilization Equipment

inadequate design of utilization equipment

cost-cutting measures which make equipment more sensitive

improper installation or application

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Who is responsible for PQ?

Utilities

to provide reliable service and voltage within specified limits

Customers

to buy less sensitive electronic devices

commercial and industrial customers should understand their power environment and purchase equipment from manufacturers who are aware of PQ issues

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Who is responsible for PQ? (continued)

Manufacturers

to produce products which will operate properly on the electromagnetic environment of a typical power system

Derating

required of induction motors in presence of voltage unbalance

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0 1 2 3 4 5

OPERATION ABOVE 5 % VOLTAGE UNBALANCE IS NOTRECOMMENDED BY NEMA STANDARDS

CE 2006 #1, NEMA DERATE.EP

PERCENT VOLTAGE UNBALANCE

DE

RA

TIN

G F

AC

TOR

Voltage unbalance at many pointson radial distribution circuits will exceed 1 %.

In old days, many inductionmotors would operate satisfactorily with voltage unbalances up to 3.0 %.

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Utility Power Quality Programs

1996 PQ survey of utilities done by PTI:

80% of utilities had PQ programs for commercial and industrial customers, 62% also had programs for residential customer

29% of utilities charged for PQ consulting

PQ programs were usually reported as effective

PQ programs

monitoring (mainly, large customer loads)

educational programs

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Power Quality Standards

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Power Quality Standards (continued)

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Some Disturbances and Corresponding Standards

Transients

ANSI/IEEE C62

IEEE Std 1100

Harmonics

IEEE Std 519

Voltage sags

IEEE Std P1346

CBEMA / ITIC tolerance curves

Voltage Flicker

IEEE Std 519

IEEE Std 141

GE Flicker Curve


Tab 20 -

Voltage Unbalance, Flicker and Transients

Distribution Systems Engineering –

Course 1

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Siemens Energy Inc., Power Technologies International 17-2

Voltage Unbalance Under Steady-State Conditions

Voltage levels are not the same on all three phases of a feeder at the same moment in time

Distribution systems are typically unbalanced•

The load demand at each phase is not the same

•

The current flow in the phase conductors is not the same

•

Line is not symmetrical•

The voltage drop is different for each phase

•

The voltage on the substation bus is unbalanced

This results in a voltage unbalance between the phases, and between the phases and ground

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Unbalanced transformerbank (open-wye

open-delta) causes unbalanced line currents on primary side as well as current in the primary multi-grounded neutral conductor

Voltage Unbalance Under Steady-State Conditions (continued)

LIGHTING LEG TRANSFORMER

POWER LEG TRANSFORMERPRIMARY NEUTRAL

PRIMARY PHASEWIRES

Note:

Transformer bank is on a two-phase tap line supplied from a three-phase four-wire multi-

grounded neutral circuit.

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Basic Definition

Voltage Unbalance In percent

AVE

max

VVx 100

Where: MAXVΔ = The maximum deviation from the average phase-to-phase voltage

AVEV = The average phase-to-phase voltage 3

|V||V||V| cabcab

Vab

, Vbc

, and Vca

are the three phase-to-phase voltages

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Example: Suppose a customer connected to the end of a 240 V three-phase service and assume that at the PCC the phase-to-

phase voltages are

|Vab

| = 230 volts|Vbc

| = 232 volts|Vca

| = 225 volts

Then: VAVE = (230 + 232 + 225) / 3 = 229 volts

∆V1

= |230 –

229| = 1 volt∆V2

= |232 –

229| = 3 volts∆V3

= |225 –

229| = 4 volts∆VMAX = 4 volts

Consequently: Voltage unbalance = (4/229)·100 = 1.75 %

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ANSI C84.1 Voltage Standards

Recommendation: Voltage unbalance at the PCC or service entrance shall not exceed 3% under no load conditions

The PCC is the point of common coupling, typically at the meter or service entrance equipment

The electric utilities are responsible only for satisfying the service entrance or PCC voltage requirements.

Customers are responsible for maintaining proper voltage downstream of the service entrance or PCC!

Classification Range A Range B Service Voltage 114 to 126 volts 110 to 127 volts

Utilization Voltage 110 to 125 volts 106 to 127 volts

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Voltage Unbalance –

Alternate Definition and Limit

CBA VaVaVV 21 31

CBA VaVaVV 22 31 2

321120 jea

Oj

100*%1

22 V

Vd

%2% 2 d

• NEGATIVE-SEQUENCE VOLTAGE UNBALANCE (d2

)

V2

= MAGNITUDE OF NEGATIVE-SEQUENCE VOLTAGE

V1

= MAGNITUDE OF POSITIVE-SEQUENCE VOLTAGE

• GIVEN THREE PHASE-TO-PHASE

VOLTAGES

VA

, VB

, AND VC (PHASORS WITHBOTH MAGNITUDE AND ANGLE):

• RECOMMENDED LIMIT FOR d2

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By knowing Ea

, Eb

and Ec

it is possible with “chart”

to determine the angle θ

and the unbalance factor d2

. Chart is applicable only when there are no zero-sequence components in the three voltages. From Westinghouse T&D Reference Book

Voltage Unbalance –

Alternate Calculation Method From Chart

EXAMPLE:Ea

= 235.0, Eb

= 230.0, Ec

= 222.0Eb

/Ea

= 0.979 Ec

/Ea = 0.945FROM CHART:

d2

= |V2

| / |V1

| = 0.034

Θ

= 37 Degrees

FROM EXACT CALCULATIONS:|V2

|| / |V1

| = 0.0330Θ

= 37.54 Degrees

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Voltage Flicker

VOLTAGE FLICKER IS:

Voltage Drop as Seen By Customers

Visible With Incandescent lights and some CFL’s

Complaints Normally From Residential Customers

Much Lower in Magnitude Than A Fault Caused Voltage Sag –

Usually Only a Few Volts on a 120-Volt Bas

Noticeable at Low Levels and Annoying at Higher Levels

VOLTAGE FLICKER DOES NOT:

Normally Does Not Cause Equipment Failure or Downtime

Does Not Damage Other Customers Equipment

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Voltage Flicker

• CAUSE-FLUCTUATING LOADS1.

ARC FURNACES2.

WELDERS3.

RECIPROCATING COMPRESSORS4.

ROCK CRUSHERS5.

SAWMILLS6.

CAR SHREDDERS

Note:1.

Flicker is worst at fluctuating load, anddecreases at points up stream from theflicker source.

• EFFECT OF VOLTAGE FLICKERCAN CAUSE VARIATION IN LAMPLIGHT OUTPUT THAT CAN BE EITHER PERCEPTIBLE OR ANNOYING TO THEEND USER

• RAPID CHANGES IN THE RMS VOLTAGE

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Fluctuations and Dips

• EXAMPLE OF WAVEFORM PRODUCING VERY OBJECTIONABLE LAMP FLICKER

ΔV = 1.10 -

0.90 = 0.20 PER UNIT

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GE Flicker Curve

Notes:1.

Based upon square-wave changes to supply voltages at indicated frequencies (see previous chart).

2.

From tests run by GE and utilities in 1930 with incandescent bulbs.3.

Used by 69 % of utilities based on 1985 IEEE survey.

• DEFINES BASED ON TESTS BORDERLINES OF VISIBILITY AND IRRITATION WITHINCANDESCENT LIGHTS

FUNCTION OF PERCENT VOLTAGE DIP AND FREQUENCY OF DIPS

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Permissible Flicker Limits (Con Edison)

• FROM 1958 EEI T&D COMMITTEE MEETING

Notes:Upper stair case curves apply to radial services and underground

networks.Lower stair case curve applies to primary distribution lines.

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Measuring Voltage Flicker The Flicker Meter

Siemens Energy


The IEC 61000-4-15 flickermeter

standard was developed in Europe and later adopted in the U.S. as IEEE 1453-2004. The measurement methodology described in the IEC standard more accurately accounts for complex voltage fluctuations encountered in actual practice by including the effects of multiple flicker sources, frequencies and varying voltage modulation waveforms. In addition, the flickermeter

approach standardizes flicker monitoring across different manufacturers–IEC 61000-4-15 compliant instruments should all produce the same results for a given flicker excitation.

The real advantage of the flickermeter

method is inherent in its ability to accurately model the human flicker perception. This rather complex modeling is accomplished by five signal processing blocks described in the IEC standard, which represent the lamp-eye-brain response to light flicker –

the response of a lamp to supply voltage variations, the perception of the human eye and the memory characteristics of the human brain.

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Measuring Voltage Flicker The Flicker Meter

Siemens Energy


The flickermeter

system provides several measurement outputs. IFL, or instantaneous flicker level, represents the real time voltage modulation modified by the lamp-eye-brain response. This output can be plotted as a time interval graph and is useful for tracking down sources of voltage fluctuations.A statistical analysis block completes the human perception system by providing short and long term flicker severity indexes. Short term flicker severity Pst

is evaluated over a 10 minute observation period and is used to

evaluate disturbances caused by flicker sources with short duty cycles.

According to the IEEE 1453 standard, a Pst

value of 1.0 represents the system compatibility level, the level below which customer complaints are not likely to occur. Pst

is therefore commonly used to evaluate whether the measured voltage fluctuations are severe enough to cause flicker complaints.Long term flicker Plt

is derived from 12 successive Pst

values, or two hours, and is more suitable for evaluating the combined effect of several randomly operating loads such as welders or motors over longer periods of

time. A Plt

value of 0.8 is considered the system compatibility limit according to IEEE 1453.

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Oscillatory Transient -

Capacitor Switching

Closing capacitor switch produceshigh-frequency inrush current andassociated high frequency componentin the system voltages, that decay exponentially with time

L

CVrms

SUBSTATIONBUS FEEDER

IMPEDANCE

Vbus

CAPBANK

CE 2006 D#2, Circuit Cap Sw Transient.FCW

S

LFRF

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Oscillatory Transient –

Inductive Load Switching

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Impulsive Transient -

Lightning Surges

BOTH MEASUREMENTSMADE ON CIRCUIT OR PTSECONDARY WITH A NOMINAL VOLTAGE OF120 VOLTS RMS OR 169.7VOLTS CREST


Tab 21 -

Harmonics, Notching and Noise Distribution Systems Engineering –

Course 1

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Siemens Industry

Inc., Siemens Power Technologies International 18-2

Voltage Notching

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Electrical Noise

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Harmonics

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Harmonics (continued)

Harmonics are multiples of the fundamental frequency

Like the waves in a pond, they will add or subtract to the fundamental

Under and Over voltageFUNDAMENTAL

TOTAL

THIRD HARMONIC

FIFTH HARMONIC

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• COMBINATION OF FUNDAMENTAL AND FIRST THREE ODD HARMONICS

unitperOrderHarmonic

PeakHarmonic 1

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• COMBINATION OF FUNDAMENTAL AND FIRST THREE ODD HARMONICS-

Harmonics lagged by 30 degrees from zero of fundamentalunitper

OrderHarmonicPeakHarmonic 1

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• COMBINATION OF FUNDAMENTAL AND FIRST THREE ODD HARMONICS-

Harmonics lagged by 60 degrees from zero of fundamental

unitperOrderHarmonic

PeakHarmonic 1

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Harmonic Distortion Factor

Distortion Factor in %

Each harmonic component contributes to the overall distortion of

the fundamental frequency wave

Each harmonic component can be expressed in percent of the amplitude of the fundamental frequency wave

Total harmonic distortion (THD) is the distortion factor including all relevant harmonic components (usually from 2nd to 50th)

100

%

wavelfundamentatheofAmplitudeAmplitudesComponentHarmonictheofSquarestheofSum

THD

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Calculation of THD

Example: Consider the voltage waveshape

shown below

Voltage Waveform at F9: phase A

5 10 15 20 25 30 35 40 45 50

0

0.5

1

0

-0.5

-1

Time (ms)

Voltage (pu)

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Calculation of THD (continued)

A harmonic spectral analysis of this wave indicates the following components:-

a fundamental frequency wave (60Hz) of magnitude 1 pu-

a 5th harmonic (300Hz) wave of magnitude 0.14 pu-



a 13th harmonic (780Hz) wave of magnitude 0.03 pu

Then:

%9.18100

103.0)03.0(12.014.0

%2222

THD

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Calculation of THD (continued)

• THEORETICAL TOTAL WAVE CONSIDERING FUNDAMENTAL, 5TH, 7TH, AND 11TH

HARMONICFROM PREVIOUS EXAMPLE

FUNDAMENTAL = 1.0 PU5TH

HARMONIC = 0.14 PU7TH

HARMONIC = 0.12 PU11TH

HARMONIC = 0.03 PU

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TVs

Computers

Fluorescent lights

Dimmers for incandescent lights

HVDC terminals

UPS Systems

AC adjustable speed motor drives

Battery Chargers (Electric Cars)

Transformers (magnetizing current)

Harmonic Sources

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Fluorescent Lighting System V-I Waves

OLD STYLE WITH FERRORESONANTLIGHTING BALLAST

TYPICAL SCREW-IN COMPACT FLUORESCENT LAMP

VOLTAGE: BLUE CURVECURRENT: RED CURVE

DISPLACEMENT POWER FACTOR ≈

40 % Total Harmonic Distortion = 19 %



SLIGHTLY LEADTotal Harmonic Distortion = 120 %

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Fluorescent Lighting System V-I Waves (continued)

FLUORESCENT LAMPS WITH ELECTRONICBALLASTS



UNITY Total Harmonic Distortion = 49 %

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Harmonics in Balanced Three-Phase Four- Wire Multi-Grounded Neutral Systems

Balanced Three-Phase System

Current waveform in each phase is identical

Fundamental component of current in each phase is displaced by 120 degrees from that in any other phase

5th, 7th, 11th, 13th, 17th, 19th, etc

Harmonic currents are either positive- or negative-sequence

No harmonic currents in neutral return path (multi-grounded neutral of primary system and earth)

3rd, 9th, 15th, 21st, etc

Harmonic currents are zero-sequence

At each harmonic, current in neutral return path is three-times that in the phase

Do not pass from secondary to primary of delta (primary) wye-grounded (secondary) transformer

Do pass from secondary to primary of wye-grounded wye-grounded transformer (flow in neutral conductor of primary system)

Siemens Industry


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ttIA 3sin1.0)sin(0.1

)

32(3sin1.0)

32sin(0.1 ttIB

)

32(3sin1.0)

32sin(0.1 ttIC

ϕA

ϕB

ϕC tIRESIDUAL 3sin3.0

RESIDUAL IS 3RD

HARMONIC

100 % Fundamental, 10 % Third Harmonic

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• ZERO-SEQUENCE HARMONIC TRANFER THROUGH DISTRIBUTION TRANSFORMERS

I3RD3

I3RD

I3RD

I3RD

N 1

I3RDN

NO ZERO-SEQUENCE HARMONICSIN PRIMARY PHASE CONDUCTORS OR IN PRIMARY NEUTRAL CONDUCTOR.

LOADS ZERO-SEQUENCE HARMONICSCIRCULATE IN DELTA WINDING.

I3RD3

I3RD

I3RD

I3RD

1

I3RD3

I3RD3

n

I3RDn

I3RDn

I3RDn

I3RDn3

I3RDn3

ZERO-SEQUENCE HARMONICS INPRIMARY PHASE CONDUCTORS AND IN PRIMARY NEUTRALCONDUCTOR (3 TIMES THAT INPRIMARY PHASE CONDUCTORS)

PTI 2010, D#1, Harmonic Transfer Thru Dist Xfrs.FCW

LOADSIDE

LOADSIDE

0

00

0

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Harmonics Produced Problems

Lighting Systems

High intensity discharge lamps outside voltage threshold can shut down

Transformers and Capacitor Banks

Resonances

Transformer derating

required with high harmonics (K Factor)

kVAr

rating of capacitor bank exceeded due to harmonic current

Other problems

Nuisance fuse operations

Device missoperations

Telephone interference (rural systems-old days)

Equipment heating•

Eventual Component failure

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IEEE 519

IEEE established a Standard for harmonic measurement and control

IEEE Std. 519

It specifically set

Requirements for Utilities•

voltage

Requirements for Customers•

current

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IEEE Std 519 Voltage Requirements

For periods less than one hour, limits may be increased by 50%.

Bus Voltage at PCC

Individual Distortion

(%)

Total Distortion THD (%)

138kV 1 1.5

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IEEE Std 519 Current Requirements

AS THE STIFFNESS OF THE UTILITY SUPPLY SYSTEM INCREASES, THE LOAD IS ALLOWED TO GENERATE MORE HARMONIC CURRENTS.


Tab 22 –

Voltage Sags, Voltage Swells, Momentary Interruptions

Distribution Systems Engineering –

Course 1

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Voltage Swell

This can occur, for instance, on the healthy (unfaulted) phases of a multi-grounded neutral distribution system during a single-line-to-ground fault

Duration of Swell

is typically between ½

cycle to 1 second

LINE-TO-GROUND VOLTAGE

1.0 PER UNIT1.25 PER UNIT

1.0 PER UNIT

CE DE 2010, Voltage Wave Sag.FCW

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Voltage Swell –

Unfaulted

Phase-to-

Ground Voltages

For Single Phase-to-Ground Fault on Phase A

Z1

= POSITIVE-SEQUENCE IMPEDANCEAT FAULT POINT

Z0

= ZERO-SEQUENCE IMPEDANCE ATFAULT POINT

Θ1 = POSITIVE-SEQUENCE IMPEDANCEANGLE AT FAULT POINT

Θ0 = ZERO-SEQUENCE IMPEDANCEANGLE AT FAULT POINT

unitperZZ

ZZaVB01

012

2

unitperZZ

ZZaVC01

01

2

23

21

23

21

1202

120

jea

jea

o

o

j

j

• UNFAULTED Φ-TO-GROUNDVOLTAGE AT FAULT POINT

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Momentary Interruption

Time in Cycles forLoss of voltage

Typically Caused By a Circuit Recloser

or Circuit Breaker Opening and Successfully Reclosing Due to a Temporary (Transient) Fault

LINE-TO-NEUTRAL VOLTAGE

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Momentary Interruption (continued)

• PERCENTAGE OF DEVICES THAT WERE ABLE TO SUCCESSFULLY RIDE THROUGH A MOMENTARY INTERRUPTION OF THE GIVEN

DURATION

DEVICEMOMENTARY INTERRUPTION DURATION

(SECONDS / CYCLES)0.5 / 30 2.0 / 120 16.7 / 1000

Digital Clocks 70 % 60 % 0

Microwave Ovens 60 % 0 0

VCR 50 % 37.5 % 0

Computer 0 0 0

FROM: POWER QUALITY ASSURANCE MAGAZINE, PP 296-310, 1990

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Momentary Interruptions (continued)

Equipment

is sensitive and can not ‘ride through’

resulting in the machine shutting down

System solutions

faster reclosing

fewer faults (tree trimming, animal & bird guards, better lightning protection)

elimination of fuse saving with feeder breaker instantaneous tripping in substation

installation of circuit reclosers

in main feeder and on major branches

closed bus tie breakers in substation (prevents momentary interruptions from loss of subtransmission

sources)

Customer solutions

static transfer switch, UPS

employ spot network systems

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Momentary Interruptions (continued)

• SYSTEM MEASURES TO REDUCE NUMBER OF MOMENTARY INTERRUPTIONS:1.

ELIMINATE INSTANTANEOUS TRIPPING OF FEEDER BREAKER 52-1 IN ATTEMPTINGTO PREVENT FUSE BLOWING FOR TEMPORARY FAULTS ON LATERALS. THIS MAY RESULT IN MORE PERMANENT OUTAGES FOR CUSTOMERS SERVED FROM FUSEDLATERALS.

2.

INSTALL RECLOSER IN MAIN FEEDER SO THAT TEMPORARY AND PERMANENTFAULTS ON “2ND

HALF OF FEEDER 2

DO NOT CAUSE A MOMENTARY INTERRUPTIONTO CUSTOMERS ON FIRST HALF OF FEEDER.

3.

USE SINGLE-PHASE RATHER THAN THREE-PHASE RECLOSERS IN 3-PHASE LINESSUBSTATION

BUS

Disk: CE Dist Course 2006, #2, Momentary Reduction.FCW

52-1 FUSE

LATERAL

RECLOSER52-2

52-3

FEEDER 1

FEEDER 2

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Voltage Sag

An RMS reduction in the nominal AC voltage, at the power frequency, to between 10% and 90% of nominal, for durations from 1/2 cycle to 1 minute.

IEEE 1250: Guide on Service to Equipment Sensitive to Momentary Voltage Disturbances

In three-phase systems, voltage sags may be same in each phase or different, depending on fault type or disturbance

In the multi-grounded neutral system, the single line-to-ground (neutral) fault can cause voltage sags in the faulted phase, and

voltage swells in the unfaulted

phases

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Examples of Voltage Sag

Even when there isn’t a complete loss of voltage, customer equipment (industrial motors, ASD) are still impacted

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Causes of Voltage Sags In Distribution Systems

Faults in sub transmission system

Faults on adjacent distribution circuits supplied from same bus section in the distribution substation

Starting of large motors

Transfer of large loads

EXAMPLES:

84% OF SAG EVENTS RESULT IN VOLTAGE LESS THAN 82.5%

40% OF SAG EVENTS RESULT IN VOLTAGE LESS 70%

16% OF SAG EVENTS RESULT IN VOLTAGE LESS THAN 40%

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Voltage Sag on Substation Bus Single Line-to-Ground Fault on Adjacent Circuit

FAULTED FEEDER (SLG PHASE A)

UNFAULTED FEEDERS

Z0SUBZ1SUB

Disk: CE Dist Course 2006, #1SUB SAG SLG FLT.FCW

Z0FDRZ1FDRVASUB

Z1SUB

= POSITIVE-SEQUENCE IMPEDANCE LOOKING INTO SUBSTATION BUS

Z0SUB

= ZERO-SEQUENCE IMPEDANCE LOOKING INTO SUBSTATION BUS

Z1FDR

= POSITIVE-SEQUENCE IMPEDANCE OF FEEDER BETWEEN SUBSTATION & FAULT

Z0FDR

= ZERO-SEQUENCE IMPEDANCE OF FEEDER BETWEEN SUBSTATION AND FAULT

unitperZZZZ

ZZV

FDRFDRSUBSUB

FDRFDRASUB

0101

01

222

• VOLTAGE ON FAULTED PHASE AT SUBSTATION BUS, VASUB

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Voltage Sag on Substation Bus Single Line-to-Ground Fault on Adjacent Circuit (continued)

• EXAMPLE CALCULATION: 13.2 KV SYSTEM, ELN

= 7620 VOLTSOH LINE, SLG FAULT ON ΦA 1.25 MILES FROM SUBSTATION

• SYSTEM DATA:AVAILABLE 3-Φ

FAULT CURRENT ON SUB BUS = I3P

= 15,000 AMP, X/R = 20AVAILABLE SLG FAULT CURRENT ON SUB BUS = ISLG

= 15,750 AMP, X/R = 20

Z1FDR

= (0.198 + j 0.583 Ω/MILE)*1.25 MILE = 0.2475 + j 0.7288 ΩZ0FDR

=(0.485 + j 1.901 Ω/MILE)*1.25 MILE = 0.6063 + j 2.3763 Ω

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iona

lN

ovem

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2012

Siemens Industry


Voltage Sag on Substation Bus Single Line-to-Ground Fault on Adjacent Circuit

(continued)

5074.002537.0))20tan(sin())20tan(cos(150007620

))/tan(sin())/tan(cos(3

1

jaja

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P

LNSUB

tab 18 - apparent power, active power, reactive...

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