Topic 6 PowerFlow Part2

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Power Systems Analysis ECNG 3012 6-Jan-May 2010

Power Flow Studies

Scenarios

Base Case(Contingency)

Weaknesses

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Control of Power Flow

! Prime mover and excitation control.

! Switching of shunt capacitor banks, shunt

reactors, and static var systems.! Control of tap-changing and regulating

transformers.

!

FACTS elements.

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Newton-Raphson Power Flow

! Quadratic convergence"mathematically superior to Gauss-Seidel

method

!

More efficient for large networks! The Newton-Raphson equations are

cast in natural power system form

"solving for voltage magnitude and angle,given real and reactive power injections

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Newton-Raphson Method

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Newton-Raphson Method

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Newton-Raphson

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Newton-Raphson

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Power Flow Equations

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Newton-Raphson

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Jacobian Matrix

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Jacobian Terms

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Jacobian Terms

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Iterative Process

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Newton-Raphson

! Slack Bus / Swing Bus" The voltage and angle are known for this bus." bus is not included in the Jacobian matrix formation

! PV (Voltage Controlled) Bus"

have known terminal voltage and real (actual) powerinjection." the bus voltage angle and reactive power injection

are computed." bus is included in the real power parts of the

Jacobian matrix.! PQ (Load) Bus

" have known real and reactive power injections." bus is fully included in the Jacobian matrix.

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Newton-Raphson Procedure

! 1. Set flat start" For load buses, set voltages equal to the slack bus." For voltage controlled buses, set the angles equal the

slack bus or 0°.

! 2. Calculate power mismatch" For load buses, calculate P and Q injections using the

known and estimated system voltages." For voltage controlled buses, calculate P injections." Obtain the power mismatches, !P and !Q

! 3. Form the Jacobian matrix" Use the various equations for the partial derivatives

the voltage angles and magnitudes

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Newton-Raphson Procedure

!

4. Find the matrix solution" inverse the Jacobian matrix and multiply by the

mismatch power.

! compute !" and !V! 5. Find new estimates for the voltage

magnitude and angle.! 6. Repeat the process until the mismatch

(residuals) are less than the specifiedaccuracy.

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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Fast Decoupled Power Flow

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!

The matrix equation is separated into two decoupledequations" requires considerably less time to solve compared to the full

Newton-Raphson method

" JP" and JQV submatrices can be further simplified to eliminatethe need for recomputing of the submatrices during each

iteration" some terms in each element are relatively small and can be

eliminated

" the remaining equations consist of constant terms and onevariable term

" the one variable term can be moved and coupled with the

change in power variable! the result is a Jacobian matrix with constant term

elements

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Jacobian calculationscan be simplified

Off-diagonal:

! "Pi

! # j

! "Qi

! V j|V|= ! -|Vi V j|Bij

diagonal: ! "Pi

! #i

! "Qi

! Vi|V|= ! -|Vi|

2 Bii

By manipulating the equations:

-Bii -Bij …

-B ji -B jj …

-Bni … -Bnn

"#i

"# j

"#n

"Pi

|Vi|

"P j

|V j|

"Pn

|Vn|

……… …

=

-Bii -Bij …

-B ji -B jj …

-Bni … -Bnn

"|Vi|

" |V j|

" |Vn|

"Qi

|Vi|

"Q j

|V j|

"Qn

|Vn|

……… …

=

B simple to calculate Very fast calculations

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Distribution Power Flow

! Radial systems.! Ladder network.

! Relationships between current on

branches and voltage at buses.

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Topic 6 PowerFlow Part2