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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
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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
Dr Sajjad Zaidi Power System Operation and Control 4
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
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Power System Representation
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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
Dr Sajjad Zaidi Power System Operation and Control 7
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
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Modelling of Synchronous Generator Frame of Reference
Rotor frame of reference Stator frame of reference
Flux frame of reference Arbitrary frame of reference
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North Pole
Rotor frame of reference
Schematic Diagram of Synchronous Machine
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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.
Equivalent circuit of a synchronous generator
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
Equivalent circuit of a synchronous generator
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.
Equivalent circuit of a synchronous generator
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 =
Equivalent circuit of a synchronous generator
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= +
Dr Sajjad Zaidi Power System Operation and Control 20
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= +
Dr Sajjad Zaidi Power System Operation and Control 21
Transient Model The induced voltage is sum of q and d axis voltage
' '
d d d a q qE V I R I X= + +' '
q q q a d dE V I R I X= +
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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 =
Dr Sajjad Zaidi Power System Operation and Control 23
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
+ = =
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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
= =
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' '
q qdt T T= =
Model 4 It is due to presence of damper winding
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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
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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
=
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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
Dr Sajjad Zaidi Power System Operation and Control 29
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
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Governor Modeling Block DiagramChange in frequency
( ) ( )s F s =
x
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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
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( )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
= +
Dr Sajjad Zaidi Power System Operation and Control 33
( )/( ) 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
Dr Sajjad Zaidi Power System Operation and Control 34
( ) 1( ) 1
tT
e SG
P sGx s sT
= =
+
Turbine Governor Block Diagram
Dr Sajjad Zaidi Power System Operation and Control 35
Turbine Governor Block Diagram
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