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Introduction to the Power Flow Problem

Smith College, EGR 325April 3, 2006

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Objectives• Introduce the power flow problem

– Numerical solution – issues?• Investigate two power flow programs

– PowerWorld– MATPower

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Complex Power – Phasor Domain

*IVS

sincos IVjIVS

)sin(cos)0sin0(cos* jIjVIVS

V

I

IMPORTANT is the power factor angle

QjPS

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Real Power Reactive Power

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Power Flow Analysis• We know

– The system topology (the circuit diagram)– The impedance of each line– The load at each load bus (S = P + jQ)– The capability of each generator (P, V)

• We want to know– The output of each generator (S)– The voltage at each bus (V = V)– The power flow on each line (Pflow)

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Real Power Flow Equations* *

i1 1

1

i1

i1

S ( )

(cos sin )( )

Resolving into the real and imaginary parts

P ( cos sin )

Q ( sin cos

ikn n

ji i i ik k i k ik ik

k kn

i k ik ik ik ikk

n

i k ik ik ik ik Gi Dikn

i k ik ik ik ik

P jQ V Y V V V e G jB

V V j G jB

V V G B P P

V V G B

)k Gi DiQ Q

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Power Flow Analysis

• Data needs?• Uses?

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Real Power Flow Equations

• How many equations and how many unknowns?

• Numerical methods– Lack of convergence– Slack bus

• Definition• Mathematical and physical role

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Running a Power Flow Program

• Programs created in the days of FORTRAN programming

• Input data one of two standard formats– IEEE– PTI

• Output data format designed by the programmer

• ** Cases may or may not converge! **

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Running a Power Flow Program

• We will use two popular programs– MATPower

• tabular data input and output• relatively easy to use

– PowerWorld• visual• more difficult to use

• Terminology– One-line diagrams– per unit system (normalize all values)

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Power System Diagrams• Circuit vs. one-line diagram

59.7 kV

17.6 MW28.8 MVR

40.0 kV

16.0 MW16.0 MVR

17.6 MW 16.0 MW-16.0 MVR 28.8 MVR

Arrows areused to show loadsGenerators are

shown as circles Transmission lines are shown as a single line

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Power System Diagrams• Circuit vs. one-line diagram

44.94 kV

16.8 MW 6.4 MVR

40.0 kV

16.0 MW16.0 MVR

16.8 MW 16.0 MW 0.0 MVR 6.4 MVR

16.0 MVR

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Summary• Introduction to the power flow problem

and programs• Numerical methods

– Significance of lack of convergence– Slack bus