tab 1 voltage stresses - power frequency...

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Tab 1 – Voltage Stresses - Power Frequency Voltage Distribution System Engineering Course – Unit 10

Siemen

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Siemens Industry, Inc., Siemens Power Technologies International

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1-2

Power Frequency Voltage Stresses

Nominal voltage stresses Overvoltage stresses

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Nominal Voltage Stresses

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Peak vs. RMS Value of an Ideal Sine or Cosine Wave

• Steady state analysis assumes continuous perfect sine/cosine waves. • Ideal sine/cosine waves have just 1 frequency component • Peak Value = √2 times the Root Mean Square (RMS) Value

Amplitude

0 x

y

1.414

1.000 RMS

Peak

t

1/4f 1/2f 1/f 0

1-4 Siem

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1-5

Ideal Voltages of Three-phase Systems

Ideal voltages are “balanced” with the same amplitude for each phase angles displaced 120 degrees ABC or Positive sequence rotation As phasors:

VA = V0 VB = V240 VC = V120 Three-phase voltages as cosine waves:

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 90 180 270 360

degrees

A [0] B [-120] C [120]

VA

VC

VB

120°

120°

120°

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1-6

Voltage Relationships in Balanced Three-Phase Circuits

VoltsV

V LLLN 621,7

3

200,13

3

3

LLLN

VV

EXAMPLE:

VLL = 13,200 Volts

x

jy

V a

V b

V c

V ab

The relationship between balanced line-to-neutral and phase-to-phase (line-to-line) voltages: Vab=Va-Vb= |Va|(1-a2)

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1-7

Voltage relationships in a three-phase system

Line-to-Line Voltage VLL

measured between two phases

Line-to-Neutral Voltage VLN measured between one phase and neutral

(ground)

VLN

VLN

VLL A B C

NEUTRAL

CONDUCTOR

VLN

VLL

VLL

A

B

C

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1-8

Per Unit System

per unit (p.u.) instead of V or kV A per unit value is simply the actual value divided by a base, or reference value.

(pu) = (unit) base = 0.01 (%)

(unit) = (pu) base (unit)

Where is one of many variables such as V, I, S, Z, Y etc.

Current, power, impedance, admittance and many other parameters can also be expressed in per unit.

The nominal voltage is typically used as the line-to-line base voltage. Siem

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1-9

Base Voltage

VLL (kV) = V (pu) x VLL-base (kV)

VLN (kV) = V (pu) x VLN-base (kV)

VLN (kVpk) = V (pu) x VLN-pk-base (kVpk)

VLL-base is usually the nominal line to line voltage in kVRMS

Volts can also be used as the units

V

3

2 = V V 2 = V V 3 = V rmsLL peak LNrmspeakLNLL Siem

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1-10

Voltage Base Example for a 138 kV system

138 kV is the nominal line-to-line voltage 138 kV is also the line-to-line voltage base. The phase-to-ground voltage base is

The peak line-to-ground voltage at 1.00 pu is

If the voltage is at 1.05 pu (105%), then

VLL = 1.05 x 138 = 144.90 kVrms VLN = 1.05 x 79.67 = 83.66 kVrms VLN-peak = 1.05 x 112.68 = 118.31 kV

rmsbaseLN kV 67.79 = 3

381 = V

kV = = V peakLN 68.1121383

2

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1-11

Nominal and Maximum RMS Voltages

Nominal Voltage the steady state line-to-line rms voltage that names the system

Maximum System Operating Voltage

The highest voltage expected under normal operating conditions at any time and at any point of the system.

Typically higher than the nominal voltage

Equipment Maximum Voltage Rating The design level for equipment insulation Typically the maximum system operating voltage

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1-12

System Voltage Classes

LV (Low Voltage) VLL< 1 kV

MV (Medium Voltage) 1 kV < VLL< 72.5 kV

HV (High Voltage) 72.5 kV < VLL < 242 kV

EHV (Extra High Voltage) 242 kV < VLL < 1000 kV

UHV (Ultra High Voltage) 1000 kV < VLL Siem

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1-13

Class Problem – System Voltages

What are some of the system voltages used by your company? Class Nominal

VLLrms

Max operating VLLrms Equipment VLLrms 1.00 pu VLNrms 1.00 VLNpeak

LV

LV

MV

MV

MV

HV

EHV Siemen

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Overvoltage Stresses

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1-15

Steady State Overvoltages

Predominately power frequency Last indefinitely Causes:

Line-to-ground faults Open conductors Backfeeding Ferranti rise Resonance Ferroresonance

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

0 1 2 3 4 5time

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1-16

The parameters are distributed along its entire length. Each Δ has

R series resistance L series inductance C shunt capacitance G shunt conductance

very small generally ignored for power flow analysis.

Distributed Line Parameters

R L

R L

R L

C C

C

. . . . . .

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1-17

Equivalent Circuit: Short Line Model

A simple pi equivalent can represent transmission lines less than 200 km where Z = ·(R1 + jX1) Ohms

Y = ·jY1 Siemens

is the length of the line R1, X1 & Y1 are the positive sequence parameters in per unit length

Use a line parameters program (i.e LineProp) for the highest accuracy

Z

Y

2

Y

2

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1-18

Ferranti Rise Overvoltages

Long lines or cables

VE/VS = f ( XL , BC )

VS VE > VS

cL

cSE

jXjX

jXVV

C2

C2

SE-L

VV

2

2LCSE

)(1

1VV

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1-19

Resonant Overvoltages

VC/VS = f ( XL , BC , R) Usually a high impedance source & a large

capacitance System restoration Backfeeding

VS Vc > VS

cL

sc

cL

csc

jX/)jX(R-1

1V/V

jXjXR

jXVV

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1-20

0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

XL/XC

V (

pu

)

Resonant Overvoltages

VS Vc > VS

cL

scX/X-1

1V/V

0Rfor

Resonant at the power frequency when XL = XC Siem

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1-21

Backfeeding

Backfeeding occurs when a circuit is fed from a lower voltage (non-generator) system

345 kV

MV bus

This circuit could see an overvoltage when bus tie breaker opens

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1-22

Ferroresonant Overvoltages

Often a transformer energized through a series capacitance

Open Circuit Breaker Parallel Lines Open phase on a distribution feeder

VS

VT = f ( XL , BC , R)

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1-23

Overvoltages From Line-to-ground Faults

Function of System Grounding Ungrounded

• source (generator or transformer) has delta winding

Solidly Grounded • source has wye winding with neutral connected to ground

Impedance Grounded

• source has wye winding with neutral connected to ground through a reactor or resistor

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1-24

Voltages On Solidly Grounded Systems

|VCN| = VLN

|VBN| = VLN

|VAN| = 0

Z0 = Z1

C

B

A

Fault to

Ground Source transformer winding Siem

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1-25

Overvoltages On Ungrounded Systems

|VCN| = VLL

|VBN| = VLL

VAN = 0

Z0 = ∞

C

B

A

Source transformer winding Fault to ground

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1-26

Overvoltages On Impedance Grounded Systems

Air core reactor

Z0 > Z1

VBN & VCN = f( Z0 , Z1 )

|VAN| = 0

C

B

A

Fault to

Ground

ZN

Source transformer winding Siemen

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1-27

Temporary Overvoltages (TOV)

Magnitudes above rated voltage Last more than 2 cycles A high power frequency component Plus the possibility of a higher frequency component TOV ratings or capability

Curves for surge arresters Limited for most other power delivery equipment

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

0 1 2 3 4 5time

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1-28

Some Causes of Temporary Overvoltages

Ferroresonance Load Rejection Single Line to Ground Faults Line Energizing Transformer Energizing Backfeeding

EHV from MV MV from LV

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tab 1 voltage stresses - power frequency...

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