Power Flow Solution Methods

1) Gauss-Seidel method.

2) Newton-Raphson (N.R.) method.

3) Newton Decoupled method.

4) Fast Decoupled method.

The factors that may be used in comparing between above techniques are :

· Acceleration.

· Accuracy

· Speed computation time (Running time).

· Required Memory space.

· Convergence.

A comparison will be made between them after explain the algorithm of each method.

1-Gauss Seidel Method

For a preliminary understanding of the method , assume that all busses are of the p-q type except the slack bus which is of the V-δ type . since the slack bus voltage is completely specified , there's no iteration involved for this bus . for all busses except (s)

In general the current at any bus of the system can be calculated as:

from the previous equ, Vp can be expressed as:

The iteration form for the bus voltage in gauss seidel method is:

There's no iterate defined for the equation corresponding to the slack bus since its voltage is known.

2-Newton-Raphson Method

1-) For P-V bus, the mismatch is get of active power (DPi) from :

2-) For P-Q bus, the mismatch is get of active and reactive power (DQi , DPi) from:

3) Then Jacobin matrix can be established as:

4) The unknown variables are (DV, Dd) obtained from:

5) After that, we update the values of (V, d) for next iteration as:

3-Newton Decoupled Load Flow Method

According to coupling phenomena where there is strong relation between (P, d) and (Q,V) ,the power flow equations of Newton Raphson form can be rewritten as :

J2 and J3 can be neglected to get the form of the following eq :

this formula is more fast, less accurate.

4-Fast Decoupled Load Flow Method

The principle of fast decoupled load flow depends on consideration that the Jacobin matrices elements are constant values, so, we perform the inverse of Jacobin for one time only.

-The(fast decoupled load flow) FDLF model is indiacted in eqs :

For B' formation ,there are some assumptions:

1)Neglect charging elements of Transmission lines.

2)Neglect shunt capacitors ( compensators ).

3)Assume |t|Ða = 1Ða.

For B'' formation, there are also some other assumptions:

1)Take in Consideration all shunt elements of transmission lines & compensators.

2)Assume |t|Ða = tÐ0.

3)Neglect Transmission lines resistances.

Ahmad Atiia

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Power Flow Solution Methods