Nov. 2003 1

Voltage Collapse in Electrical Power Systems

by

Zivan ZabarECE Dept

Nov. 2003 2

Voltage collapse

Voltage collapse of an electric distribution network means that the system can no longer maintain voltage at the load site.

Nov. 2003 3

Electrical grid (system)

Electrical grid consists of three main components:

• Generating plants• Transmission and distribution networks• Customer loads

Nov. 2003 4

Transmission of electric power(Bonneville Power Adm.)

Nov. 2003 5

Basic Components of Power System (H. Saadat)

Nov. 2003 6

Subtransmission Grid & Low-Voltage Secondary Ntwk (W)

Nov. 2003 7

Voltage Collapse (DC circuit)

From

€

P = I2R and

€

V =E

R +r R we get:

€

V =12

E ± E2 − 4 ⋅P ⋅r( )

and

€

I =E − V

r

Nov. 2003 8

Voltage Collapse (DC circuit); cont.

Max powerat r = R

Load power

Loadvoltage Current

r1

r2 < r1

Nov. 2003 9

AC power

€

Apparent = Active + j ⋅Reactive

where:

€

S = P + jQ

€

P = V ⋅I⋅cos ϕ [W]

€

Q = V ⋅I⋅sinϕ [VAr]

€

ϕ − the phase angle between

the current and the voltage

Nov. 2003 10

Power transfer over a transmission line

Active power:

€

P =E ⋅V

Xsinθ [W]

Reactive Power:

€

Q =E ⋅V

Xcosθ−

V2

X [VAr]

Nov. 2003 11

Power transfer curves

ReactivePower

ActivePower

ReactivePower

Nov. 2003 12

Voltage collapse (AC circuit)

Power [W]:

€

PL =VS ⋅VL

Xsinθ

Reactive power [VAr]

€

QL =VS ⋅VL

Xcosθ−

VL2

X

Defining:

€

β=tanϕ

€

VL =VS

2

2− β ⋅PL ⋅X±

VS4

4− PL ⋅X PL ⋅X+ β ⋅VS

2( )

Nov. 2003 13

Voltage collapse (AC circuit) cont.

Load powerCriticalvoltage

Loadvoltage Current

€

β1=0.18PF1 = 0.98€

β2=0PF2 = 1

Nov. 2003 14

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 15

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 16

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 17

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 18

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 19

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 20

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Summary of the situation at 4:10:38

Nov. 2003 21

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 22

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 23

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 24

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 25

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 26

August 14, 2003 Blackout--Sequence of events[US/Canada Outage Task Force; 9/12/03]

Nov. 2003 27

Nov. 2003 28