transient stability studies (powertrs)
DESCRIPTION
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. Transient stability Large disturbance (First swing). - PowerPoint PPT PresentationTRANSCRIPT
TRANSIENT STABILITY STUDIES(POWERTRS)
Indonesia Clean Energy Development (ICED) project
Indonesia Wind Sector Impact AssessmentPresented by:
Dr. Balaraman, Ph.D.
Makassar, February 17 to 21, 2014
Voltage stability
Rotor angle stabilityStudy period: 0-10
sec
Mid-term/long-term stabilityStudy period: seconds to
several minutes(slow dynamics)
Small signal stability
Non-oscillatory Insufficient synchronizing torque
OscillatoryUnstable control
action
Transient stabilityLarge disturbance(First swing)
Stability
f, v, loading acceptable, load met,n-1 or n-2 contingency acceptable
f, v, loading acceptable
load met n-1 or n-2 contingency
not satisfied
f, v, loading not acceptable,
load not met
Normal
Alert Restorative
Cascaded system
syste
m In Extremis Emergency
Power System Operating States
Pool control centre
System control centre
To other systemTo other system To other system
Transmission system Power plant
DS DS DS G G G
DS: Distribution SystemG : Generator
Control Hierarchy
f Ptie Pgtotal
Schedule System generation controlLoad frequency control with
economic allocation
Other generating unitsand associated controls
Generating units control
Prime mover & control
Excitation system &control
Generator f/N or
Pg Vt
If
Pm f/N
Transmission ControlsReactive power, Voltage control,HVDC transmission and others
Pg
f Ptie Pg.total
Power System Subsystem & Controls
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
Stable Unstable
Stable Unstable
t Sec. t Sec.
t sec.t Sec.
m2
m2
m1 m1
0 0
00
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).
Stable Unstable
Stable
Unstable
Steady State Stability
J dd t
T T T N mma m e*
2
2
• 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.
Mechanical Equation
Reference Axis Stationary
m
Reference axis at sm
sm
sm
Rotor axis at rotor speed
m sm mt m : Angular displacement of the rotor in mechanical radians.
ddt
ddt
ddt
ddt
Jddt
T T N m
ddt
Angular velocity in radians per
Jddt
P P watts
Mddt
P P Approx
msm
m
m m
mm e
mm
mm
m e
mm e
2
2
2
2
2
2
2
2
2
2
sec.
( )
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
emm
sm
emm
sm
smsm
PPdt
dHS
wattsPPdt
dM
radianmechanicalperMJSHM
MVAMJS
M
S
JH
2
2
2
2
2
2
2
/21
21
ems
emm
sm
emm
sm
PPdtdH
puPPdt
dH
SPP
dtdH
2
2
2
2
2
2
2
2
2
2
2
2
2
deg
180
2
12 1 ,
22 ,
m e
m e
m e ss
m e
s
s
s
H d P P pu SwingEquationf dt
If inelectrical d rees
H d P P puf dt
H d dP Pdt dt
Let P P puH d pu t
dt HIf t H
Pm
Pe = 1 pu
• 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 KEMachine Rating
H Machine Rrating H systemMVA
H H Machine ratingSystem MVA
mech system
system mech
Inertia constant (H) is in the range 2 - 9 for various types of machines. Hence H-constant is usually defined for machine.
machineS
NWR
H
Wattslbft
lbftNWRKE
feetingyrationofRadiusRpoundsinpartrotationalofWeightW
ftlbWRInertiaofMoment
622
22
22
10550746
602
2.3221
746sec/55060
22.322
1
::
2.32
Relation between H constant and Moment of Inertia is given by:
Example :Smach = 1333 MVA, WR2 = 5820000 lb – ft2, N= 1800
RPM
= 3.2677575 pu (MJ/ MVA)On 100 MVA base : H = 1333 / 100 = 43.56 (MJ /
MVA)
13336018002
2.325820000
2110
550746 2
6
H
G1 ,H1
Pe1Pm1
G2 ,H2
Pm2Pe2
Hf
ddt
P Pm e1
21
2 1 1
2222
22
em PPdt
dfH
H Hf
d
dtP P P Pm m e e
1 22
2 1 2 1 2
PePtd
df
Hm2
2
HStored energy at rated speed in MWs
MVA rating
H = H1 + H2
Pm = Pm1 + Pm2
Pe = Pe1 + Pe2
G1 and G2 are called coherent machines.
Inertia Constant
ratingMVARPMJ
ratingMVA
JH
RPMradianmechanicalinspeedRated
mkgininertiaofMomentJ
MWsJ
wattsJ
energyKineticenergyStored
om
om
om
om
29
62
2
62
2
1048.5
1021
602sec/:
:
1021
21
MKS system
22
22
356.12.32
)(
mkgWRJ
ftlbgyrationofradiusofsquarepartrotatingofWeightWR
British units
Given
JWR
kg mt
HJ RPM
MVA ratingMWs MVA
Stored energyH MVA rating MWs
Mechanical starting timeH onds
22
62
32 21356 27547 77168
548 10
2
.. .
.( )
/
sec
MVA rating : 555WR2 : 654158 lb-ft2
Example
Non coherent machines
Hf
ddt
Pm Pe12
12 1 1
ddt
fH
P Pm e
21
21
1 1
Hf
ddt
P Pm e2
22
2 2 2
ddt
fH
P Pm e
22
22
2 2
Unit Type H ConstantHydro Unit 2 to 4
Thermal unit
2 pole – 3600 RPM 2.5 to 6
4 pole – 1800 RPM 4 to 10
Typical Values
ddt
f
HP P
fH
P P
f
d
dt
H P P P P H
H H
H HH H f
d
dtH
H HP P
HH H
P P
H HH H f
d
dtH P H P
H H
H P H P
H H
H
m e m e
m e m e
m e m e
m m e e
2
2 1 21
1 12
2 2
21 2
22 1 1 2 2 1
1 2
1 2
1 2
21 2
22
1 21 1
1
1 22 2
1 2
1 2
21 2
22 1 1 2
1 2
2 1 1 2
1 2
1
1
1
fddt
P P
Where
HH H
H HP
H P H P
H H
PH P H P
H H
m e
mm m
ee e
2122 12 12
1 2
1 212
2 1 1 2
1 2
122 1 1 2
1 2
,
Relative swing (with reference to one machine) is more important, rather than absolute swing.
Relative Plot (i-)Absolute Plot
1
o
2
3
4
3
20
1
T in sec. T in sec.
Swing curves
Relative swing (with reference to one machine) is more important, rather than absolute swing.
I
E’ = Vt + (0 + jxd’) I
E’
Vt
jxd’ I
Ref.Vt
I
E’
jxd’+
-
Classical model : (Type 1) Constant voltage behind transient reactance
E1 : Magnitude of voltage at bus1E2 : Magnitude of voltage at bus2 : 1 - 2Xs : Reactance
PE EXs
1 2 sin
jXs
E2 2E1 1
Power angle equation
Machine Parameters Synchronous : Steady state, sustained.Transient : Slowly decaying Sub-transient : Rapidly decayingE=?
X=?
X X X X X
T T
T T
d q q q d
d do
qo qo
' " "
' "
' "
0
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
Stable At s ; Pm = Pe ; net accelerating torque = 0.Let Pe decrease slightly.
increase (acceleration) comes back to original position.Stable region . Hence s is stable operating point.
veisPPdtd
fH
em 2
2
P
Pmmmm
O
Pe=Pmax sin
u
900 s 1800
Unstable
At u; Pm = Pe ; Net accelerating torque = 0 ,
Let Pe decrease slightly.
increases, (acceleration)Pe further decreases.Chain reaction never comes back to normal valueHence u is unstable operating point.
veisPPdtd
fH
em 2
2
System
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.
200 MW1.05 pu V
250 MVA250 MVA Slack bus
1 pu - V
Example :
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 Load11 kVSwitchedCapacitor
132/110 kV
Load Modeling
fo
Po
frequency
Power
· Vary the tap.· Switch on the capacitor.· Determine the response (charge) in load.· Compute the parameters.• P = P0 (CP + CI . V + CZ . V2) ( 1+Kf . f) · P varies with time, voltage andfrequency.· P0 varies with time - can be constant at agiven 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 ofmeasurements.
• 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.
• What it implies :– Initial load 10,000 MW.– Loss of generation 700 MW– Increase in load 700 MW – Frequency 49 Hz.
5.350
1100
7
:100,;
%7000,10
700
7001
700)(
)(700
pf
pf
pfoo
pfo
C
baseMVAonthenfrequencyinchangeunitpertheisfpuinisPIf
C
numberpowerCffP
loadindecreaseCfP
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
Load model Parameters
Loads
Transducer
Regulator Exciter Generator
Limiter + relay
PSS
Excitation System Components
Ref.
ControllerRegulator
Poweramplifier(Exciter) Plant
Feedback elements
Block Schematic
EtEfdVtrVer
Vref
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
AGC
Speedchanger
SpeedGovernor
Valve/gate
ElectricalSystem
Energy Supplysteam or water
TurbineGenerator
Speed
Tie line Power
Frequencies
Speed governor systems:
1/R 11TTws
ws
1T Kms D
speed
TurbineDroop(Goveror) Generator+
-
SpeedRef.
Types of Control:• Primary Control : Governor action• Secondary Control : AGC, load frequency control (For
selected generators)
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
Trip signal 49.50.4 Hz/s
48
10% load rejection
15% load rejection
50% load rejection
30% load rejection
1 Hz/s
4 Hz/s
2 Hz/s
Other measures :* Fast valving* Steam by-passing
Load shedding
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
Time in seconds
AVR & PSS
Constant Efd
AVR with no PSS
65432
90
60
30
1
Typical swing curve :
0.01
0.090
0.025
5 4 3 2 1
180
120
60
Time in Sec.
Rotor angle degrees
Integration step size : Typical value : 0.01 seconds, Range : 0.005 to 0.02 seconds
Typical swing curve :
11 1sT
ksT1
21
s=f(Efd)
sksT3
41
1
2 3k sT
PSS
+-
+
Vref
+
- EfdVT
AVR : Type 1
Efd11 1sT
ksT1
21
sk
sT sT3
4 51 1
Vs
+-
+
Vref
SE
1
2 3k sT+
-VT
VRmax
VRmin-
AVR : Type 2
VT 11001. s
k sT sTsT sT
1 2 3
4 5
1 11 1
( )
+
- +
Vref VRmax
VRmin
Efdmax
Efdmin
11 1sT
AVR TYPE – 5
ref
+
1/T31/S
+PrefP5
Pmax
C min
P-up
P-dn
1+sT2
0 k1(1+sT1)
-
+
- Pmin
C max
Steam Turbine Governing System
K1: 0.05 Pmax: 1.0T1: 0.1 Pmin: 0.0
T2: 0.03 Pup: 0.1
T3: 0.4 Pdn: -1.0
P
1/(1+sT1 ) 1/(1+sT2)
k1+k2 k3+k4
(1/1+sT3) (1/1+sT4)
k5+k6 k7+k8
Ps
Turbine Model
+
111sT-
+
-
1
2T Pmin
Pmax
Ps
ksTsT13
31.
k2
Transient Droop Compensator
Permanent Droop Compensator
ref
+
+
CminP-dn
Cmax
1s
P-up
Hydro Governor
Hydro Turbine
Ps1-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 EnhancementMethods :
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 switching8. 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, [email protected]
+1-904-923-6489, http://i-windenergy.com Dr.K.Balaraman Ph.D
CGM, [email protected]
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