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# Power Flow Problem Formulation - PowerPoint PPT Presentation

Power Flow Problem Formulation. Lecture #19 EEE 574 Dr. Dan Tylavsky. Notation: Polar Form Rep. of Phasor:. Rectangular Form Rep. of Phasor:. Specified generator power injected at a bus:. Specified load power drawn from a bus:. Specified load/generator reactive power:.

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### Power Flow Problem Formulation

Lecture #19

EEE 574

Dr. Dan Tylavsky

• Rectangular Form Rep. of Phasor:

• Specified generator power injected at a bus:

• Specified load power drawn from a bus:

• Specified voltage/angle at a bus:

• Complex Power: S

• Power Flow Problem Statement

• Given:

• Network topology and branch impedance/admittance values,

• PL & QL Values for all loads,

• Active power (PG) at all generators (but one),

• VSp=|E| at all generator buses,

• Maximum and minimum VAR limits of each generator,

• Transformer off-nominal tap ratio values,

• Reference (slack, swing) bus voltage & angle,

• Power Flow Problem Statement

• Find:

• V &  at all load buses,

• V, QG at all generator buses, (accounting for VAR limits)

• PG, QG at the slack bus.

100 MW

50MW

Network

P=100 MW

Q=20 MVAR

P=300 MW

Q=100 MVAR

P=200 MW

Q=80 MVAR

Control

Center

Without knowledge of PLoss, PG cannot be determined a priori & vice versa.

Defn: Distributed Slack Bus - Losses to the system are supplied by several generators.

Defn: Slack Bus - That generator bus at which losses to the system will be provided. (Often the largest bus in the system.)

X=3 types:

X=1

• Formulating the Equation Set.

• Necessary (but not sufficient) condition for a unique solution is that the number of equations is equal to the number of unknowns.

• For linear system, must additionally require that all equations be independent.

• For nonlinear systems, independence does not guarantee a unique solution, e.g., f(x)=x2-4x+3=0

• Multiplying both sides of above eqn. by E at the node and taking the complex conjugate,

S types:iq

i

q

SG

yiq

SL

Sir

r

yir

• The Power Balance Equation.

• Can we apply Newton’s method to these equations in complex form?

• Recall Newton’s method is based on Taylor’s theorem, which is complex form is:

• Homework: Show that the Cauchy-Rieman equations are not obeyed by the power balance equation.

• Show for homework:

Solution is slightly slower to converge than polar form but, it is possible to construct a non-diverging iterative solution procedure.

• Individually show that starting with:

You obtain:

• We’ll use this form of the equation.

• P-V Bus (not on VAR limits)

(Important: When on VAR limits, the PV bus equations are the same as the PQ bus equations)

• Slack Bus following set of equations for each bus type: