ee552 lecture 06 modeling 01

Advance Power System Operation and Control

Lecture 06Lecture 06

Modeling of Power Systems

Structure of Power System

Dr Sajjad Zaidi Power System Operation and Control 2

Control of Power System


Control Method Manual Intervention

Slow Depends on human response

Digital Control Computer Based Reliable Fast Fast Adaptive

Advantages High speed of operation Higher accuracy Optimal operation Network state scanning and monitoring Adaptive control possible Low maintenance and low operating cost


Type of Computer Control System Supervisory

The computer generates an out to change the setpoint of the controller The computer is just the decision making tool The controller is the workhorse in the control system

Controller can be an analogue or digital

Direct Control Direct Control The computer itself acts as controller Executes the decision taken by itself Types

Off line On line In line


Power System Representation


Power System at Normal Operating State Power System operates in normal state if following conditions

are satisfied: Load flow is equation is satisfied

Balance between generated and demanded power The frequency is constant The bus voltage is |Vt| is within the prescribed limit

V V V

No power system component is to be overloaded Steady State Stability Limit

It is also known as static transmission capacity, is given as


min maxi i iV V V

max

i iij

ij

V VP

X=

Modeling of System Why do we make model of any thing may be electrical or Why do we make model of any thing may be electrical or

electrical power system?electrical power system? In the present day engineering, designing and manufacturing,

computer simulations are of great significance For clear understanding Detailed analysis of system behavior

Component modeling is very important Component modeling is very important Modeling should have identical behavior as of physical system The governing mathematical equations are solved


Modelling of Synchronous Generator Frame of Reference

Rotor frame of reference Stator frame of reference

Flux frame of reference Arbitrary frame of reference


North Pole

Rotor frame of reference

Schematic Diagram of Synchronous Machine


Generator ModelingGenerator Modeling

Equivalent circuit of a synchronous generator

The internally generated voltage in a single phase of a synchronous machine EA is not usually the voltage appearing at its terminals. It equals to the output voltage V only when there is no armature current in the machine. The reasons that the armature voltage EA is not equal to the output that the armature voltage EA is not equal to the output voltage V are:1. Distortion of the air-gap magnetic field caused by the

current flowing in the stator (armature reaction);2. Self-inductance of the armature coils;3. Resistance of the armature coils;4. Effect of salient-pole rotor shapes.


Armature reaction (the largest effect):When the rotor of a synchronous generator is spinning, a voltage EA is induced in its stator. When a load is connected, a current a load is connected, a current starts flowing creating a magnetic field in machines stator. This stator magnetic field BS adds to the rotor (main) magnetic field BR affecting the total magnetic field and, therefore, the phase voltage.

Lagging load


Assuming that the generator is connected to a lagging load, the load current IA will create a stator magnetic field BS, which will produce the armature reaction voltage Estat. Therefore, the phase voltage will be

A statV E E = +The net magnetic flux will be

net R SB B B= +Rotor field Stator field

Note that the directions of the net magnetic flux and the phase voltage are the same.


Assuming that the load reactance is X, the armature reaction voltage is

stat AE jXI= The phase voltage is then A AV E jXI = Armature reactance can be modeled by the following Armature reactance can be modeled by the following circuit

However, in addition to armature reactance effect, the stator coil has a self-inductance LA (XA is the corresponding reactance) and the stator has resistance RA. The phase voltage is thus

A A A A AV E jXI jX I RI =


Often, armature reactance and self-inductance are combined into the synchronous reactance of the machine:

S AX X X= +Therefore, the phase voltage is

A S A AV E jX I RI =

The equivalent circuit of a 3-phase synchronous generator is shown.

The adjustable resistor Radj controls the field current and, therefore, the rotor magnetic field.

Phasor diagram of a synchronous generator

Since the voltages in a synchronous generator are AC voltages, they are usually expressed as phasors. A vector plot of voltages and currents within one phase is called a phasor diagram.

A phasor diagram of a synchronous generator with a unity power factor (resistive load)

Lagging power factor (inductive load): a larger than for leading PF internal generated voltage EA is needed to form the same phase voltage.

Leading power factor (capacitive load).

For a given field current and magnitude of load current, the terminal voltage is lower for lagging loads and higher for leading loads.

Power and torque in synchronous generators

The real output power of the synchronous generator is

3 cos 3 cosout T L AP V I V I = =The reactive output power of the synchronous generator is

3 sin 3 sinQ V I V I = =3 sin 3 sinout T L AQ V I V I = =Recall that the power factor angle is the angle between V and IA and not the angle between VT and IL.In real synchronous machines of any size, the armature resistance RA

Power and torque in synchronous generators

Then the real output power of the synchronous generator can be approximated as

3 sinAout

S

V EP

X

We observe that electrical losses are assumed to be zero since the resistance is We observe that electrical losses are assumed to be zero since the resistance is neglected. Therefore:

conv outP PHere is the torque angle of the machine the angle between V and EA.

The maximum power can be supplied by the generator when = 900:

max

3 AS

V EP

X

=

Steady State Model It is from the basic concept of electrical machines

A group of synchronous machines or a part of power system can be represented as a single equivalent synchronous machine

' '

d d d a q qE V I R I X= + +' '

q q q a d dE V I R I X= +


Steady State Model It is from the basic concept of electrical machines

A group of synchronous machines or a part of power system can be represented as a single equivalent synchronous machine

' '




Transient Model The induced voltage is sum of q and d axis voltage

' '




Model 1 In this model,

the machine has been assume to have the magnitude of constant voltage behind the d-axis transient reluctance only

q axis transient flux linkage is neglected for being small Mechanical System equations have been considered:

1m e

d dP P D =


m eP P Ddt M dt=

2 od fdt

pi=

M = Angular MomentumH = inertia constantfo = base frequency = angular frequency

Pm = Mechanical PowerPe = Electrical PowerD = damping coefficient = rotor angle

Model 2 In model 0 and 1, electrical dynamics have not been considered

( ) ( )' ''' '

f d d d qf qq

d d

E X E I EE EdEdt T T

+ = =


Model 3 This is further detailed model Transient effects both in the d and q axis have been considered

( )' ''' '

q q q dd dX E I EdE E

dt T T

= =


' '

q qdt T T= =

Model 4 It is due to presence of damper winding


Modeling of Synchronous Generator in a Network The generator models are made with a reference rotating with

its own rotor The real and imaginary components can be form as


Modeling of Synchronous Generator in a Network This can be formed as

and

cos sinsin cos

r q

im d

V VV V

=

cos sinsin cos

q r

d im

V VV V

=


The vector V can also be represented as

( ) jq dV V jV e = +

Modeling of Synchronous Generator in a Network Power equations of for a salient pole alternator can be

modelled by any of the model. Power equation in steady State is given as

21 1

sin sin 22d q d

E V VP

X X X

= +

Power equation in transient state is given as


2'

' ' '

1 1sin sin 2

2g d q d

E V VP

X X X

= +

Governor Modelling The model of generator will be complete only with the modeling

of few other components Governor Excitation Control

Governor When load increases,

The speed of generator reduces slightly The speed of generator reduces slightly The governor reacts to this and increases steam flow increases steam flow from boiler to the

turbine The speed of turbine increases

The increased steam flow Causes reduced boiler pressure Fuel, air and water follow supply increases

As the boiler inertia is high, the effect of load changes only influences the generator


Governor Modeling Block DiagramChange in frequency

( ) ( )s F s =

x


Opening of steam ValveConnected

Change in Power

R = Speed regulation of the governorKSG = gain of the speed governorTSG = time constant of the speed

ex

Governor Model

If Pc =1 and =0, then

11

SGe c

SG

Kx P

sT R

= + ( ) ( )s F s =

ex

K then


( )1

SGe c

SG

Kx P

sT =

+

( )1SG

e

SG

Kx

s sT =

+ ( )/

1/SG SG

SG

K Ts s T

=

+

11SG SG

SG

K Ks

T

=

+

Governor Model

The governor action has been modeled as transfer function

( ) ( )s F s =

ex

11SG SG

e

SG

K Kx

s

T

= +


( )/( ) 1 SGt Te SGx t K e =

Turbine Modelling Turbine dynamics are import as they affect overall response of

the generating plant to load changes Type of turbine affects it dynamics

Non reheat type steam turbine After passing through the control valve, the high pressure steam enters

the turbine via steam chest The steam chest introduces the delay of TT in the steam flow The transfer function becomes


( ) 1( ) 1

tT

e SG

P sGx s sT

= =

+

Turbine Governor Block Diagram


ee552 lecture 06 modeling 01

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