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8/21/2019 PSA12 Rep Complete HS12

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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 = 6.39 cycles

Critical fault clearing time


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No damping


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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



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( )

Fault Current Calculation

Waveform of fault current

Modelling

Computational methods



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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 !
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Schne Weihnachtszeit !

Merry Christmas !

psa12 rep complete hs12

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