Lecture 22Power System Protection, Transient Stability

Professor Tom OverbyeDepartment of Electrical and

Computer Engineering

ECE 476

POWER SYSTEM ANALYSIS

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Announcements

Be reading Chapters 9 and 10 After exam read Chapter 11 HW 9 is 8.4, 8.12, 9.1,9.2 (bus 2), 9.14; do by Nov 10 but does not need

to be turned in. Start working on Design Project. Firm due date has been extended to

Dec 1 in class Second exam is on Nov 15 in class. Same format as first exam, except

you can bring two note sheets (e.g., the one from the first exam and another) Exam/solution from 2008 will be posted on website shortly Exam covers through Chapter 10

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In the News: Boulder municipalization

• Last week Boulder, CO narrowly voted to move forward with municipalization of their electric grid• Currently Boulder is in the Xcel Energy electric service territory

(Xcel is a large Investor Owned Utility)

• Xcel has recently decided not to continue funding the Boulder “SmartGridCity” initiative, which has cost $45 million, triple its original cost.

• Xcel does not wish to sell its electric grid in Boulder, saying it would be extremely expensive for Boulder to go on their own.

Source: NY Times 11/3/11; Thanks to Margaret for pointing out this story

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Power System Protection

Main idea is to remove faults as quickly as possible while leaving as much of the system intact as possible

Fault sequence of events1. Fault occurs somewhere on the system, changing the

system currents and voltages

2. Current transformers (CTs) and potential transformers (PTs) sensors detect the change in currents/voltages

3. Relays use sensor input to determine whether a fault has occurred

4. If fault occurs relays open circuit breakers to isolate fault

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Power System Protection

Protection systems must be designed with both primary protection and backup protection in case primary protection devices fail

In designing power system protection systems there are two main types of systems that need to be considered:

1. Radial: there is a single source of power, so power always flows in a single direction; this is the easiest from a protection point of view

2. Network: power can flow in either direction: protection is much more involved

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Radial Power System Protection

Radial systems are primarily used in the lower voltage distribution systems. Protection actions usually result in loss of customer load, but the outages are usually quite local.

The figure showspotential protectionschemes for a radial system. Thebottom scheme ispreferred since itresults in less lost load

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Radial Power System Protection

In radial power systems the amount of fault current is limited by the fault distance from the power source: faults further done the feeder have less fault current since the current is limited by feeder impedance

Radial power system protection systems usually use inverse-time overcurrent relays.

Coordination of relay current settings is needed toopen the correct breakers

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Inverse Time Overcurrent Relays

Inverse time overcurrent relays respond instan-taneously to a current above their maximum setting

They respond slower to currents below this value but above the pickup current value

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Inverse Time Relays, cont'd

The inverse time characteristic provides backup protection since relays further upstream (closer to power source) should eventually trip if relays closer to the fault fail

Challenge is to make sure the minimum pickup current is set low enough to pick up all likely faults, but high enough not to trip on load current

When outaged feeders are returned to service there can be a large in-rush current as all the motors try to simultaneously start; this in-rush current may re-trip the feeder

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Inverse Time Overcurrent Relays

Relays havetraditionally beenelectromechanicaldevices, but aregradually beingreplaced by digital relays

Current and timesettings are ad-justed using dialson the relay

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Protection of Network Systems

In a networked system there are a number of difference sources of power. Power flows are bidirectional

Networked system offer greater reliability, since the failure of a single device does not result in a loss of load

Networked systems are usually used with the transmission system, and are sometimes used with the distribution systems, particularly in urban areas

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Network System Protection

Removing networked elements require the opening of circuit breakers at both ends of the device

There are several common protection schemes; multiple overlapping schemes are usually used

1. Directional relays with communication between the device terminals

2. Impedance (distance) relays.

3. Differential protection

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Directional Relays

Directional relays are commonly used to protect high voltage transmission lines

Voltage and current measurements are used to determine direction of current flow (into or out of line)

Relays on both ends of line communicate and will only trip the line if excessive current is flowing into the line from both ends

– line carrier communication is popular in which a high frequency signal (30 kHz to 300 kHz) is used

– microwave communication is sometimes used

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Impedance Relays

Impedance (distance) relays measure ratio of voltage to current to determine if a fault exists on a particular line

1 1

12 12

Assume Z is the line impedance and x is the

normalized fault location (x 0 at bus 1, x 1 at bus 2)

V VNormally is high; during fault

I IxZ

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Impedance Relays Protection Zones

To avoid inadvertent tripping for faults on other transmission lines, impedance relays usually have several zones of protection:

– zone 1 may be 80% of line for a 3 fault; trip is instantaneous– zone 2 may cover 120% of line but with a delay to prevent

tripping for faults on adjacent lines– zone 3 went further; most removed due to 8/14/03 events

The key problem is that different fault types will present the relays with different apparent impedances; adequate protection for a 3 fault gives very limited protection for LL faults

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Impedance Relay Trip Characteristics

Source: August 14th 2003 Blackout Final Report, p. 78

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Differential Relays

Main idea behind differential protection is that during normal operation the net current into a device should sum to zero for each phase

– transformer turns ratios must, of course, be considered

Differential protection is used with geographically local devices

– buses– transformers– generators

1 2 3 0 for each phase

except during a fault

I I I

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Other Types of Relays

In addition to providing fault protection, relays are used to protect the system against operational problems as well

Being automatic devices, relays can respond much quicker than a human operator and therefore have an advantage when time is of the essence

Other common types of relays include– under-frequency for load: e.g., 10% of system load must be shed if

system frequency falls to 59.3 Hz– over-frequency on generators– under-voltage on loads (less common)

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Sequence of Events Recording

During major system disturbances numerous relays at a number of substations may operate

Event reconstruction requires time synchronization between substations to figure out the sequence of events

Most utilities now have sequence of events recording that provide time synchronization of at least 1 microsecond

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Use of GPS for Fault Location

Since power system lines may span hundreds of miles, a key difficulty in power system restoration is determining the location of the fault

One newer technique is the use of the global positioning system (GPS).

GPS can provide time synchronization of about 1 microsecond

Since the traveling electromagnetic waves propagate at about the speed of light (300m per microsecond), the fault location can be found by comparing arrival times of the waves at each substation

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Power System Transient Stability

In order to operate as an interconnected system all of the generators (and other synchronous machines) must remain in synchronism with one another– synchronism requires that (for two pole machines) the

rotors turn at exactly the same speed

Loss of synchronism results in a condition in which no net power can be transferred between the machines

A system is said to be transiently unstable if following a disturbance one or more of the generators lose synchronism

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Generator Transient Stability Models

In order to study the transient response of a power system we need to develop models for the generator valid during the transient time frame of several seconds following a system disturbance

We need to develop both electrical and mechanical models for the generators

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Example of Transient Behavior

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Generator Electrical Model

The simplest generator model, known as the classical model, treats the generator as a voltage source behind the direct-axis transient reactance; the voltage magnitude is fixed, but its angle changes according to the mechanical dynamics

'( ) sinT ae

d

V EP

X

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Generator Mechanical Model

Generator Mechanical Block Diagram

m

D

e

( )

mechanical input torque (N-m)

J moment of inertia of turbine & rotor

angular acceleration of turbine & rotor

T damping torque

T ( ) equivalent electrical torque

m m D e

m

T J T T

T

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Generator Mechanical Model, cont’d

s

s s

s s

In general power = torque angular speed

Hence when a generator is spinning at speed

( )

( ( ))

( )

Initially we'll assume no damping (i.e., 0)

Then

m m D e

m m D e m

m m D e

D

m e

T J T T

T J T T P

P J T P

T

P P

s( )

is the mechanical power input, which is assumed

to be constant throughout the study time period

m

m

J

P

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Generator Mechanical Model, cont’d

s

s s

s

s

( )

rotor angle

( )

inertia of machine at synchronous speed

Convert to per unit by dividing by MVA rating, ,

( ) 2

m e m

m s

mm m s

m m

m e m

B

m e s

B B B

P P J

t

ddt

P P J J

J

S

P P JS S S

2 s

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Generator Mechanical Model, cont’d

s

2

2

( ) 22

( ) 1(since 2 )

2

Define H per unit inertia constant (sec)2

All values are now converted to per unit

( ) Define

Then ( )

m e s

B B B s

m e ss s

B B s

s

B

m es s

m e

P P JS S S

P P Jf

S S f

JS

H HP P M

f f

P P

M

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Generator Swing Equation

This equation is known as the generator swing equation

( )

Adding damping we get

( )

This equation is analogous to a mass suspended by

a spring

m e

m e

P P M

P P M D

kx gM Mx Dx

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Single Machine Infinite Bus (SMIB)

To understand the transient stability problem we’ll first consider the case of a single machine (generator) connected to a power system bus with a fixed voltage magnitude and angle (known as an infinite bus) through a transmission line with impedance jXL

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SMIB, cont’d

'

'

( ) sin

sin

ae

d L

aM

d L

EP

X X

EM D P

X X

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SMIB Equilibrium Points

'

Equilibrium points are determined by setting the

right-hand side to zero

sinaM

d L

EM D P

X X

'

'th

1

sin 0

Define X

sin

aM

d L

d L

M th

a

EP

X X

X X

P XE

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Transient Stability Analysis

For transient stability analysis we need to consider three systems

1. Prefault - before the fault occurs the system is assumed to be at an equilibrium point

2. Faulted - the fault changes the system equations, moving the system away from its equilibrium point

3. Postfault - after fault is cleared the system hopefully returns to a new operating point

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Transient Stability Solution Methods

There are two methods for solving the transient stability problem

1. Numerical integration this is by far the most common technique, particularly

for large systems; during the fault and after the fault the power system differential equations are solved using numerical methods

2. Direct or energy methods; for a two bus system this method is known as the equal area criteria mostly used to provide an intuitive insight into the

transient stability problem

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SMIB Example

Assume a generator is supplying power to an infinite bus through two parallel transmission lines. Then a balanced three phase fault occurs at the terminal of one of the lines. The fault is cleared by the opening of this line’s circuit breakers.

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SMIB Example, cont’d

Simplified prefault system

1

The prefault system has two

equilibrium points; the left one

is stable, the right one unstable

sin M th

a

P XE

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SMIB Example, Faulted System

During the fault the system changes

The equivalent system during the fault is then

During this fault nopower can be transferredfrom the generator to the system

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SMIB Example, Post Fault System

After the fault the system again changes

The equivalent system after the fault is then

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SMIB Example, Dynamics

eDuring the disturbance the form of P ( ) changes,

altering the power system dynamics:

1sina th

Mth

E VP

M X