The document discusses load flow studies and the Gauss-Siedel method for solving power flow equations. Load flow studies calculate voltage drops, bus voltages, and power flows under various conditions to determine if voltages remain within limits and equipment is not overloaded. The Gauss-Siedel method iteratively solves power flow equations represented by a non-linear algebraic equation using the bus admittance matrix and known real and reactive power values at buses to calculate unknown bus voltages until converging on a solution. An example applies the Gauss-Siedel method with an acceleration factor to a three bus system to calculate voltages after the first iteration.

1. Gauss Siedel method
of Load flow studies
Presenter:
Abdul Azeem
M. Tech (Power System & Drives)
Department of Electrical Engineering
Z.H.C.E.T.
Aligarh Muslim University
Aligarh UP

2. Load/Power Flow studies
 Load-flow studies are performed to determine the steady-state
operation of an electric power system. It calculates the voltage
drop on each feeder, the voltage at each bus, and the power
flow in all branch and feeder circuits.
 Determine if system voltages remain within specified limits
under various contingency conditions, and whether equipment
such as transformers and conductors are overloaded.
 Load-flow studies are often used to identify the need for
additional generation, capacitive, or inductive VAR support, or
the placement of capacitors and/or reactors to maintain system
voltages within specified limits.
 Losses in each branch and total system power losses are also
calculated.
 Necessary for planning, economic scheduling, and control of an
existing system as well as planning its future expansion of
system.

3. Power Flow Equation
Note: Transmission lines are
represented by their equivalent pi
models (impedance in p.u.)
Applying KCL to this bus results
in
(1)
Fig. 1. A typical bus of the power system.

4. (2)
The real and reactive power at bus
i is
Substituting for Ii in (2) yields
Equation (5) is an algebraic non linear equation which must be solved by
iterative techniques

5. Gauss-Seidel method
 Equation (5) is solved for Vi solved iteratively
Where yij is the actual admittance in p.u.
Pi
sch and Qi
sch are the net real and reactive powers in p.u.
In writing the KCL, current entering bus I was assumed positive. Thus
for:
Generator buses (where real and reactive powers are injected), Pi
sch and
Qi
sch have positive values.
Load buses (real and reactive powers flow away from the bus), Pi
sch and
Qi
sch have negative values.

6. Eqn.5 can be solved for Pi and Qi
The power flow equation is usually expressed in terms of the
elements of the bus admittance matrix, Ybus , shown by upper case
letters, are Yij = -yij, and the diagonal elements are Yii = ∑ yij.
Hence eqn. 6 can be written as

7. Iterative steps:
•Slack bus: both components of the voltage are specified. 2(n-1)
equations to be solved iteratively.
• Flat voltage start: initial voltage of 1.0+j0 for unknown voltages.
• PQ buses: Pi and Qi are known. with flat voltage start, Eqn. 9 is solved
for real and imaginary components of Voltage.
•PV buses: Pi
sch and [Vi] are known. Eqn. 11 is solved for Qi
k+1 which is
then substituted in Eqn. 9 to solve for Vi
k+1

8. Example
 A three bus system are shown in figure. The
relevent per unit values of admittences on 100 MVA
base are indicated on the diagram and bus data
are given in table-
Form Ybus and determine the voltage at bus 2 and
bus bus 3 after the first iteration using Gauss-
Siedel method.Take the acceleration factor 1.6.
(Power System Analysis by Ashfaq Hussain, page
no. 380)

10.  We first calculate the element of the
Ybus
 Y11 =sum of admittences of all elements connected
to node 1=-j3-j4=-j7
 Y22 =sum of all admiteneces connected to bus 2=-
j3-j4=-j8
 Y33=sum of all the admittences connected to bus
3=-j4-j5=-j9
 Y12=Y21=-(-j3)=j3
 Y23=Y32=-(j5)=j5
 Y31=Y13=-(-j4)=j4


14. THANKS