EE 451

Power System Stability

Power system operates in synchronous mode

Power system is subjected to a wide range of disturbances

(small and large)

- Loads and generation changes

- Network changes

- Faults and outages of equipment

Hence, the stability of the power system will be affected.

Power system stability involves the study of the dynamics of

the power system under disturbances.

From the classical point of view, power system instability can

be seen as loss of synchronism (i.e., some synchronous

machines going out of step)when the system is subjected to a

particular disturbance.

CIGRE-IEEE Def. of Power System Stability:

Power system stability is the ability of an electric power

system, for a given initial operating condition, to regain a state

of operating equilibrium after being subjected to a physical

disturbance, with most system variables bounded so that

practically the entire system remains intact.

Stability involves study of dynamics of the system about an

equilibrium-initial operating condition.

Power system is highly non-linear system Stability study

study of non-linear dynamics of large system.

Stability (can be defined only in terms of)

Initial operating condition

Nature and magnitude of disturbance

Def. applies to an interconnected power system as a whole.

Most of the time we are interested in stability of a particular

generator or a group of generators

In our study we will focus on:

1- Steady-State Stability

2- Transient Stability

Steady state stability of power systems results from gradual

system changes.

Example: Gradual load increase as in the addition of MW at load

terminals or in gradual load decrease, as in steam change at the prime

mover power.

Power systems in general and alternators in particular have steady state

stability limit beyond which if subjected to gradual load changes will

loss steady state stability.

The power system is capable to resist the changes that occurs after the

disturbance and hence remain in stable form that is capable of

maintain equilibrium.

Example of sudden system changes (Transient Stability) are:

Fault occurrences, autoreclosure schemes, energization process of a

T.L. and de-energization of a T.L.

Recalling some definitions:

- Steady state stability is the ability of the power system network to

remain or to stay in equilibrium following a gradual system

change.

- Steady state stability limit is the maximum power transfer of that

system without loss of equilibrium.

Machines (Generator / Motor)

PS

Pi

Pf

Pl

PO Turbin

e

Generator

Tm

Tm

Te

Te

Pi : Input power to alternator (Generator) (i.e. mechanical power input)

PO : Output power from alternator (Generator) (i.e. electrical power input)

Pf : Internal generated field power

PS : Mechanical losses due to (friction …etc)

Pl : Electrical stator losses

Power balanced equation for generator

Pf = Pi - PS (1)

PO = Pf - Pl (2)

From (1) & (2)

PO = Pi - PS - Pl Power balanced under equilibrium state

PS

Pi

Pf

Pl

PO Turbin

e

Generator

Synchronous Motor

(1) &

(2)

From (1) & (2) under equilibrium

PS Pm

Pf

Pl

Pe Motor

\ \

\

I- Generator feeding an Inductive load:

(1)

Internal field power is:

Sf = Pf + jQf = ExI*

ExI* =

Substituting for , the angle

Inductive

Load

E 0

Zs s I -

V -

i.e.

for large turbo-alternators:

Therefore: and the power angle diagram will be:

Pf

Pfmax

0

Generator output Power PO

Take V as a reference,

Substituting the complementary of the impedance angle

The power output from the generator is given as:

Since is generally a small angle for large turbo-alternator

At

, PO = Pmax

Pmax is the steady-state stability limit of the alternator

Pf

0

PO (MW)

Load angle

Margin for safety operation

Pmax

P

II- Alternator Feeding an Infinite Bus System:

Infinite bus means:

1- Voltage is constant

2- Frequency is constant

3- Internal Impedance is zero

Infinite

Bus

PO =

PO

PO

Pmax

0

PO (MW)

Load angle

III- Two Machine System:

Eg = V + I Zg

Em = V + I Zm

Generator power

Motor power

V

I

M Em Eg

If is small then steady state stability limit:

Pgmax =

= - Pm max

Where is the load angle

-Pm max

Pg max

P

IV- Transmission System:

ES ErT1 T2

VS Vr

Assumption:

Ignore system resistance and consider system reactance only.

System power transfer (point to

point) is:

P =

Xl

XS Xr

Power transfer between individual components:

At stability limit:

Pmax =

Where Xt : is known as the system transfer reactance.

Power angle diagram for transmission network

Pmax

P

Improvement of steady state stability limit

1- Improving excitation system

2- Reduce system transfer reactance

3- Parallel circuit arrangement

4- Series Compensation