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Power System Analysis
Highlights HS2012
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Topics
Power flow analysis
Short circuit current calculation
Dynamics and control
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The Swiss High Voltage Grid (Source: swissgrid)
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Ceuta
HVDC
Population > 400 Mio.Installed capacity: 350 GW
Annual generation: 2200 TWh
ENTSO-E RG Continental Europe(Former UCTE)
380 kV
220 kV
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Power Flow
Steady State Process Model
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Flows on transmission line:
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Power Flow for a Branch
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( )
( )
km km
km km
G Y
B Y
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Gauss-Seidel Iteration 1
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Gauss-Seidel Iteration 2
Gauss Iteration
Gauss-Seidel Iteration
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Newton-Raphson Algorithm
P Fl E ti
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Power Flow Equations
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De-coupled Power Flow
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Linearized Power Flow
(DC Power Flow)
An approximative power flow solution can be
obtained by linearizing the power flow
equations. Assumptions:
1. Angle differences between buses are small
2. Line series resistances are neglected
3. All voltage magnitudes in the system are
equal, normally 1 p.u.
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Short Circuit Current Calculations
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Three-phase Short-Circuit on a Transmission Line
Assumptions:
1. The system can be approximated by a Thevenin
equivalent
2. The voltage source of the Thevenin equivalent is
constant during the short circuit (amplitude and phase)
3. Line capacitances are neglected and the system
is unloaded before the fault
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Definition of Short Circuit Capacity, SCC
Note: Uis here the line-to-line rms voltage
SCC is normally given in MVA or p.u.
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Relationship between reactances
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Other models of synchronous machines
Sometimes other values of the reactance are used:
e.g.
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Short Circuit Studies
>
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V lt h b t d i t
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Voltage sources have been converted into
equivalent current sources
V
C
S iti (1)
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Superposition (1)
S perposition (2)
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Superposition (2)
Power Flow Calculation
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Unknown
Known
Unknown
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Known
Unknown
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Power System Dynamics and Control
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Figure 8.2.Classification of power system stability.
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Western USA August 1996
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Western USA July 1996
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Figure 10.1.Schematic description of powers and torquesin synchronous machines.
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Figure 11.1.Synchronous machine connected to infinite bus.
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Figure 11.2.Equivalent electric circuit of asynchronous machine connected to an infinite bus.
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Figure 11.3.Diagram showing the variation of electric and
mechanical power for the system in eq. (11.7).
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Fault occursFault clearing
Critical point
Reclosure
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Fault clearing time = 4 cycles
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Fault clearing time = 6 cycles
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Fault clearing time = 8 cycles
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Fault clearing time = 6.39 cycles
Critical fault clearing time
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Fault clearing time = 4 cycles
No damping
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Fault clearing time = 7 cycles
Reclosure after 20 cycles
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Figure 11.9.Application of the equal area criterion after
a disturbance.
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1857 -1918
Lyapunov function of SMIB system, Fig. 11.4
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tf = 5 c :
V = 0.2015
tf = 5.5 c :
V = 0.2571
Lyapunov function of SMIB system, Fig. 11.4
D = 0
Vp
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Figure 8.2.Classification of power system stability.
Long Term Voltage Stability
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Long Term Voltage Stability
Short Term Voltage Stability
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Short Term Voltage Stability
Contributing factors:
Induction motors (Air conditioning)
(LCC) HVDC, Power Electronics
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Figure 13.1. Simple system for analysis of voltage stability.
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Figure 13.2. Relation between active power
and voltage magnitude in the load node.
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/2 /2
/2
Figure 13.4. Voltage phasors for the system in Figure 13.3.
Voltage stability indicators (1)
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Voltage stability indicators (1)
Voltage Sensitivity Factor for node i(VSFi)
Stability criterion:
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Figure 13.5. Nose curves for different values of the
power factor of the load of the system in Figure 13.1.
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Constant power load, kp = 0
VSF > 0; Stable
VSF < 0; Unstable
VSF =
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Constant impedance load, kp = 2
VSF > 0; Stable
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Figure 13.8. Nose curve for undisturbed system, curve 1,
and for a system where the sending end voltage has been
increased by 5%, curve 2.
III
III Load Control:II III
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Figure 13.9. Nose curve for undisturbed system, curve 1,
and for a system where the sending end voltage has been
increased by 5%, curve 2.
I
II
III
F
Load Control:
II III F
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Figure 14.2. The different generation reserves in a power system.
Sicher, Normal
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Figure 14.6. The different operating states of a power system.
Gefhrdet
Gestrt
Kritisch
Wiederaufbau
N-1
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Table 14.1. Characteristics of the different operating states
of a power system.
Operating
Margins
Rating
Limits
Pgen= Pload + Ploss
Normal State
Alert State
Emergency State
Extremis State
X
XX
XXX
The essence of the smart grid
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g
Advanced metering
infrastructure
Fully responsive
load control
Phasor measurement units
Wide area monitoring and
control
From Prof. Ian Hisken, University of Michigan
Important Topics (1)
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p p ( )
Power Flow Calculation:
Node types: PU, PQ, Slack
Power flow equations
Problem definition
Use of power flow calculation in planning and
operation
Solution methods
Important Topics (2)
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( )
Fault Current Calculation
Waveform of fault current
Modelling
Computational methods
Important Topics (3)
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Dynamics
Stability
Angle stability
Equal Area Criterion (SMIB)
Voltage stability
System states
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More about these issues in:
227-0528-00L,Power Systems Dynamics and
Control
(Systemdynamik und Leittechnik in derelektrischen Energieversorgung)
FS 2012,
Marek Zima, G.A.
Master and Semester Projects
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http://www.eeh.ee.ethz.ch/en/eeh/education/courses.html
Students project
or contact us (ETL G level)
Apero 11 December, 2012
Schne Weihnachtszeit !
http://www.eeh.ee.ethz.ch/en/eeh/education/courses.htmlhttp://www.eeh.ee.ethz.ch/en/eeh/education/courses.htmlhttp://www.eeh.ee.ethz.ch/en/eeh/education/courses.html8/21/2019 PSA12 Rep Complete HS12
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Schne Weihnachtszeit !
Merry Christmas !
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