TRANSIENT STABILITY STUDIES
(POWERTRS)
Indonesia Clean Energy Development (ICED) project
Indonesia Wind Sector Impact Assessment
Presented by:
Dr. Balaraman, Ph.D.
Makassar, February 17 to 21, 2014
Stability
Rotor angle stability
Study period: 0-10
sec
Mid-term/long-term stability
Study period: seconds to
several minutes
(slow dynamics)
Voltage stability
Small signal stability
Transient stability
Large disturbance
(First swing)
Non-oscillatory
Insufficient synchronizing torque
Oscillatory
Unstable control
action
Power System Operating States
f, v, loading acceptable,
load met,
n-1 or n-2 contingency
acceptable
Restorative
Normal
f, v, loading
acceptable
load met
n-1 or n-2 contingency
not satisfied
Alert
Cascaded
system
syste
In Extremis
m
Emergency
f, v, loading not
acceptable,
load not met
DS: Distribution System
G : Generator
Control Hierarchy
Pool control centre
To other system
To other system
System control centre
Transmission system
DS
DS
DS
Power plant
G
G
G
Power System Subsystem & Controls
f
Schedule
Ptie
Pgtotal
System generation control
Load frequency control with
economic allocation
Generating units control
Other generating units
and associated controls
Prime mover & control
Excitation system &
control
f/N or
Pg
Pm
If
f/N
Generator
Vt
Pg
Transmission Controls
Reactive power, Voltage control,
HVDC transmission and others
f
Ptie
Pg.total
Power System Stability
• Ability of a power system to remain in synchronism
• Classification of transients : Electromagnetic and
Electromechanical
Stability classification
• Transient stability : Transmission line faults, sudden load
change, loss of generation, line switching etc.
• Dynamic stability : Slow or gradual variations. Machine,
governor - Turbine, Exciter modelling in detail.
• Steady state stability : Changes in operating condition. Simple
model of generator.
Transient Stability: First swing and Multiple Swings
m2
m1
0
m2
0
t Sec.
Stable
0
t Sec.
Unstable
0
t sec.
Stable
t Sec.
Unstable
m1
Assumptions :
• Synchronous speed current and voltage are
considered.
• DC off set currents, harmonics are neglected.
• Symmetrical components approach.
• Generated voltage is independent of machine speed.
• Circuit parameters are constant at nominal system
frequency. (Frequency variation of parameter
neglected).
Steady State Stability
Stable
Unstable
Stable
Unstable
Mechanical Equation
d 2 m
J*
 Ta  Tm  Te
2
dt
Nm
• J : Moment of inertia of rotor masses (kg-mt2 )
• m : Angular displacement of rotor w.r.t. a stationary
axis (mechanical radians)
• t : Time (seconds)
• Tm : Mechanical or Shaft Torque ( N-m )
• Te : Net electrical torque (N-m )
• Ta : Net accelerating torque (N-m)
•
• For generator, Tm and Te are +ve.
 sm
Rotor axis at rotor
speed
m
 sm
Reference Axis
Stationary
Reference axis at  sm
m : Angular displacement of the rotor in mechanical radians.
 m   sm t   m
d m
d m
 sm 
dt
dt
d 2 m d 2  m

2
dt
dt 2
d 2 m
J
 Tm  Te N  m
dt 2
d
 m  m  Angular velocity in radians per sec.
dt
J m
d 2 m
 Pm  Pe watts
dt 2
d 2 m
M
 Pm  Pe ( Approx )
2
dt
Where M : Inertia constant = at synchronous speed in Joules-sec per
mechanical radian.
Constant is defined as the ratio of stored Kinetic Energy
in Mega Joules at synchronous speed and machine
rating in MVA
1
1
2
J sm
M  sm
H 2
2
MJ / MVA
S
S
2H S
M
MJ p er m ech a n icara
l d ia n
M
 sm
d 2 m
2
 Pm  Pe wa tts
dt
2 HS d 2 m
 Pm  Pe
2
 sm d t
2 H d 2 m Pm  Pe

2
 sm d t
S
2H d  m
 Pm  Pe p u
2
 sm d t
2
2 H d 2
 Pm  Pe
2
s dt
H d 2
 Pm  Pe pu
2
 f dt
Swing Equation
If  in electrical d deg rees
H d 2
 Pm  Pe pu
180 f dt 2
2 H d
d
 Pm  Pe 
 s
s dt
dt
Let Pm  Pe  1 pu

2 H d
1 pu ,   s t
s dt
2H
If t  2 H ,   s
Pe = 1 pu
Pm
• At t = 0, breaker is opened.
• Initially Pe = 1 pu on machine rating Pm = 1pu and
kept unchanged.
• In 2H seconds, the speed doubles.
H
Stored KE
Machine Rating
H mech  Machine Rrating  H system  systemMVA
Machine rating
 H system  H mech 
System MVA
Inertia constant (H) is in the range 2 - 9 for various
types of machines. Hence H-constant is usually
defined for machine.
Relation between H constant and Moment of Inertia
is given by:
WR 2
Mom entof Inertia
lb  ft 2
32.2
W :Weightof rotationalpartin pounds
R:Radiusof gyrationin feet
1 WR 2  2N 
KE 
ft lb


2 32.2  60 
550 ft lb/ sec746Watts
2
1 WR 2  2N  746
6


10
2 32.2  60  550
H
S machine
2
Example :
Smach = 1333 MVA, WR2 = 5820000 lb – ft2, N= 1800
RPM
 746 6 1 5820000  21800
 55010 2 32.2  60 
H
1333
2
= 3.2677575 pu (MJ/ MVA)
On 100 MVA base : H = 1333 / 100 = 43.56 (MJ /
MVA)
Pe1
Pm1
G1 ,H1
Pe2
Pm2
G2 ,H2
H1 d 2 1

 Pm1  Pe1
2
f
dt
H 2 d 2 2
 2 Pm 2 P e 2
f  dt
 H 1  H 2  d  
 f  2   Pm1  Pm2    Pe1  Pe2 

 dt
2
H d 2
Pm Pe
2
f dt
H = H1 + H2
Pm = Pm1 + Pm2
Pe = Pe1 + Pe2
G1 and G2 are called coherent machines.
Inertia Constant
Stored energy at rated speed in MWs
H
MVA rating
MKS system
S to reden erg yKin eticen erg y

1
2
J  om  wa tts
2

1
2
J  om  1 0 6 MWs
2
J :Mo m en o
t f in ertiainkgm 2
 om :Ra tedsp eedinm ech a n icara
l d ia n/ sec
1
2
J  om  1 0 6
H  2
MVAra tin g
9
5.4 8 1 0
 J RPM 2 


 MVAra tin g 
2
RPM
60
British units
Given
WR 2  Weightof rotatingpart  squareof radiusof gyration(lb  ft 2 )
WR 2
J 
1.356kg  m 2
32.2
Example
MVA rating : 555
WR2 : 654158 lb-ft2
WR 2
J
 1.356  27547.77168
32.2
H  5.48  10
6
J ( RPM ) 2

MVA rating
Stored energy
 H  MVA rating 
Mechanical starting time
 2H 
sec onds
MWs
kg  mt 2
MWs / MVA
Typical Values
Unit Type
H Constant
Hydro Unit
2 to 4
Thermal unit
2 pole – 3600 RPM
2.5 to 6
4 pole – 1800 RPM
4 to 10
Non coherent machines
H 1 d 2 1
 Pm1  Pe1
2
f dt
H2 d2 2
 Pm2  Pe2
2
f dt
d 2 1
dt 2
f

Pm1  Pe1 

H1
d 2 2  f

Pm2  Pe2 

2
H2
dt
d2
dt
2
 1   2  

f
H1
 Pm1  Pe1  
f
Pm2  Pe 2
H2



2
H 2  Pm1  Pe1    Pm2  Pe 2  H 1
1 d 1   2

2
f
H1 H 2
dt
2
H1 H 2
1 d  1   2 
H2
H1


 Pm1  Pe1  
 Pm2  Pe2 
2
H 1  H 2 f
H1  H 2
H1  H 2
dt


d 2 1   2
H1 H 2
1
H P  H 1 Pm2 H 2 Pe1  H 1 Pe 2


 2 m1

2
H 1  H 2 f
H1  H 2
H1  H 2
dt
H d 2 12

 Pm12  Pe12
f
dt2
Where ,
H
H1 H 2
H1  H 2
Pe12 
Pm12 
H 2 Pm1  H 1 Pm2
H1  H 2
H 2 Pe1  H 1 Pe 2
H1  H 2
Relative swing (with reference to one machine) is more important, rather than
absolute swing.
Swing curves
3
2
1
4
3
o
2
0
1
T in sec.
Absolute Plot
T in sec.
Relative Plot (i-)
Relative swing (with reference to one machine) is
more important, rather than absolute swing.
Classical model : (Type 1)
Constant voltage behind transient reactance
I
E’
jxd’
+
Ref.
E’
Vt
jxd’ I
-
Vt
I
E’ = Vt + (0 + jxd’) I
Power angle equation
jXs
E1 1
E1 E 2
P
sin 
Xs
E1 : Magnitude of voltage at bus1
E2 : Magnitude of voltage at bus2
 : 1 - 2
Xs : Reactance
E 2  2
X=?
E=?
Machine Parameters
Synchronous : Steady state, sustained.
Transient
: Slowly decaying
Sub-transient : Rapidly decaying
X d  X q  X q ' X q " X d "
Td 0 ' Tdo "
Tqo '  Tqo "
Typical values
Parameter
Hydro (pu)
Thermal (pu)
xd
0.6 - 1.5
1.0 - 2.3
xq
0.4 - 1.0
1.0 - 2.3
xd’
0.2 - 0.5
0.15 - 0.4
xq’
-------
0.3 - 1.0
xd”
0.15 - 0.35
0.12 -0.25
xq”
0.2 - 0.45
0.12 -0.25
Td0’
1.5 - 9.0 s
3.0 -10.0 s
Tq0’
-------
0.5 - 2.0 s
Td0”
0.01 - 0.05 s
0.02 - 0.05 s
Tq0”
0.01 - 0.09 s
0.02 - 0.05 s
Ra
0.002 - 0.02
0.0015 - 0.005
Stability
P
Pe=Pmax sin
Pm
mm
m
O
s
900
u 1800

Stable
At s ; Pm = Pe ; net accelerating torque = 0.
Let Pe decrease slightly.
H d 2
Pm Pe is  ve
 f dt 2
 increase (acceleration)
 comes back to original position.
Stable region . Hence s is stable operating point.
Unstable
At u; Pm = Pe ; Net accelerating torque = 0 ,
Let Pe decrease slightly.
H d 2
Pm Pe is ve
2
 f dt
 increases, (acceleration)
Pe further decreases.
Chain reaction   never comes back to normal value
Hence u is unstable operating point.
Infinite bus
• Generator connected to infinite bus.
• High inertia. H  compared to other machines in the
system.
• Frequency is constant.
• Low impedance. Xd’ is very small.
• E’ is constant and Vt is fixed.
• Infinite fault level symbol.
System
Example :
200 MW
1.05 pu V
250 MVA
250 MVA
Slack bus
1 pu - V
H = 3.2 , Z = 10% on own rating , Xd1 = 25% , tap = 1, Ra = 0.0
and neglect R.
• Establish the initial condition.
• Perform the transient stability without disturbance.
• Open the transformer as outage & do the study.
• How long the breaker can be kept open before closing, without
losing synchronism.
Load Modeling
132/110 kV
Switched
Capacitor
Load
11 kV
Load

Vary the tap.

Switch on the capacitor.

Determine the response (charge) in
load.
P

Compute the parameters.
o
2
•
P = P0 (CP + CI . V + CZ . V ) ( 1+Kf . f) w
e Po

P varies with time, voltage and
r
frequency.

P0 varies with time - can be constant at a
given time of a day.

CP, CI, CZ & Kf are constants.

V & f are known at any time instant.

P is known from measurements.

Solve the non linear problem over a set of
measurements.
frequency
fo
• Let the load be 10,000 MW. i.e. P0 = 10,000
• Let for 1 Hz change in frequency, let the load change be 700 MW.
Po f  C f
p
 7 0 0( d ecrea seinlo a d)
Po ( f  f o )  C f
p

 700
7 0 0p o wern u m b er
1
700

 7%
1 0,0 0 0
If Pisin p u; f isth e p eru n itch a n g e
in freq u en cy,th eno n1 0 0MVAb a se :
Cf
p
Cf
p

7
1 0 0 3.5
1
50
• What it implies :
–
–
–
–
Initial load 10,000 MW.
Loss of generation 700 MW
Increase in load
700 MW
Frequency 49 Hz.
Load model Parameters
Load model parameters
Measurement based approach
Input: Connected load
Measurement: P,V, f over a period
Out put: Parameters
Component based approach
Industrial
Commercial
residential
Agricultural
Loads
Excitation System Components
Transducer
Ref.
Exciter
Regulator
Generator
PSS
Limiter + relay
Vref

Ver Controller
Regulator
Vtr Power
amplifier
(Exciter)
Feedback elements
Block Schematic
Et
Efd
Plant
Reactive Power Control
•
•
•
•
•
Synchronous generators
Overhead lines / Under ground cables
Transformers
Loads
Compensating devices
Control devices
• Sources /Sinks --- Shunt capacitor, Shunt inductor
(Reactor), Synchronous condenser, and SVC.
• Line reactance compensation --- Series capacitor
• Transformer -----OLTC, boosters
Speed governor systems:
Tie line Power
AGC
Electrical
System
Frequencies
Energy Supply
steam or water
Speed
changer
Speed
Governor
Valve
/gate
Speed
Turbine
Generator
Types of Control:
•
•
Primary Control : Governor action
Secondary Control : AGC, load frequency control (For
selected generators)
Speed
Ref.
+
Turbine
Droop(Goveror)
1  Tws
1  Tws
1/R

Generator
Tms
1
 KD
speed
Under Frequency operation :
Vibratory stress on the long low pressure turbine blades
 Degradation in the performance of plant auxiliaries say,
induction motor
Limitations
•
•
•
•
Only maximum spinning reserve can be achieved
Turbine pickup delay
Boiler slow dynamics
Speed governor delay
Load shedding
Trip signal 49.5
0.4 Hz/s
10% load rejection
1 Hz/s
15% load rejection
2 Hz/s
4 Hz/s
30% load rejection
50% load rejection
48
Other measures :
* Fast valving
* Steam by-passing
Modules in a program
• Data reading
• Initialization
•
•
•
•
•
•
– Steady state load flow
– Control block parameter AVR, Gov., Machine, Motor, PSS, HVDC, SVC.
Disturbance model
Control block modeling
Machine modeling
Load flow solution
Protective relay modeling
Special functions
– Cyclic load
– Arc furnace
– Re-closure
• Results Output
– Report
– Graph
Typical swing curve :
Constant Efd
90
60
30
AVR & PSS
AVR with no PSS
1
2
3
Time in seconds
4
5
6
Typical swing curve :
180
Rotor angle
degrees
0.090
120
0.025
60
0.01
1
2
3
4
5
Time in Sec.
Integration step size : Typical value : 0.01 seconds, Range :
0.005 to 0.02 seconds
AVR : Type 1
s=f(Efd)
Vref
VT
1
1  sT1
+

-

+
k1
1  sT2

+
PSS
sk 3
1 sT4
1
k 2  sT3
Efd
AVR : Type 2
Vref
VT
1
1  sT1
SE
VRmax
+

-
+
Vs
-
k1
1  sT2
-

+
VRmin
sk3
1  sT4 1  sT5 
1
k 2  sT3
Efd
AVR TYPE – 5
Vref
VT
1
1  0.01s
VRmax
+

+
k1 1 sT2 1 sT3 
1
1  sT1
(1 sT4 )1 sT5 
VRmin
Efdmax
Efdmin
Steam Turbine Governing System
ref
+
Pref
1+sT2
0 k1(1+sT1)

+
P-up
C max
-
+

1/S
1/T3
-

Pmax
Pmin
C min
P-dn
K1: 0.05
Pmax: 1.0
T1: 0.1
Pmin: 0.0
T2: 0.03
Pup: 0.1
T3: 0.4
Pdn: -1.0
P5
Turbine Model
k1+k2
P



k3+k4
k5+k6
k7+k8
Ps
1/(1+sT1 )
1/(1+sT2)
(1/1+sT3)
(1/1+sT4)
Hydro Governor
ref
+
+


-
-
P-up
Cmax
1
1  sT1
1
T2
Pmax
1
s
Ps
Pmin
Cmin
P-dn

+

k1 .
sT3
1 sT3
Transient Droop Compensator
+
k2
Permanent Droop Compensator
Hydro Turbine
Ps
1-sT1
1+0.5sT1
DM
T1 (T) : 1.0
Transient Stability Enhancement
Philosophy
• Minimize the disturbance influence by
minimizing the fault severity and duration.
• Increase the restoring synchronizing forces.
• Reduce accelerating torque.
Transient Stability Enhancement
Methods :
1. High speed fault clearing.
2. Reduction of transmission system reactance.
3. Regulated shunt compensation.
4. Dynamic Braking.
5. Reactor switching.
6. Independent pole operation of circuit breaker.
7. Single pole switching
8. Fast valving.
9. Generator tripping.
10. Controlled system separation and load shedding.
11. High speed excitation systems.
12. HVDC transmission link control.
Major references used in the development of
Transient Stability Studies Module
1. Dommel, N. Sato “Fast Transient Stability Solutions”, IEEE
Transactions on
Power Apparatus and Systems, 1972, PP 1643 1650.
2. W. Dommel, “Digital computer solution of electromagnetic transients in
single and multiphase networks”, IEEE Transactions on Power
Apparatus and Systems, April 1969, Vol. PAS-88, PP 388 - 399.
3. IEEE Committee Report, “Dynamic Models for Steam and Hydro
Turbines in Power System Studies”, IEEE PES Winter Meeting, New
York, Jan./Feb. 1973. (Paper T 73 089-0).
4. IEEE Committee Report, “Proposed Excitation System Definitions for
Synchronous Machines”, IEEE Transactions on Power Apparatus and
Systems, Vol. PAS-88, No. 8, August 1969.
5. IEEE Committee Report, “Computer representation of excitation
systems”, IEEE Transactions Power on Apparatus and Systems,
June 1968, Vol. PAS-87, PP 1460 - 1464.
For further information please contact:
Office Address of ICED-USAID
(Indonesia Clean Energy Development – United States Agency for International Development)
•ICED-USAID Jakarta Office: Tifa Building, 5th Floor, Jl. Kuningan Barat No. 26 Jakarta 12710;
Phone/Facsimile: +62 21 52964445/ 52964446
•ICED-USAID Medan Office: Jl. Tengku Daud No. 7A Medan 20152;
Phone/Facsimile: +62 61 4519675/ 4519058
Contact Person:
Pramod Jain, Ph.D.
President, Innovative Wind Energy, Inc.
pramod@i-windenergy.com
+1-904-923-6489, http://i-windenergy.com
Dr.K.Balaraman Ph.D
CGM, PRDC
balaraman@prdcinfotech.com
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