topic 6 powerflow part2
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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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Fast Decoupled Power Flow
!
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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Fast Decoupled Power Flow
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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