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International Journal of Exploring Emerging Trends in Engineering (IJEETE)

Vol. 04, Issue 06, NOV-DEC, 2017 Pg. 280 – 294 WWW.IJEETE.COM

ISSN – 2394-0573 All Rights Reserved © 2017 IJEETE Page 280

COMPARATIVE ANALYSIS OF TWO DIFFERENT LOAD FLOW ITERATIVE

TECHNIQUES USING AYEDE 330/132KV SUBSTATION AS CASE STUDY

Adu, Michael Rotimi

The Federal University of Technology, Akure

School of Engineering and Engineering Technology

Department of Electrical and Electronics Engineering

[email protected] or [email protected]

Cell Phone: +2348060352786

Abstract

Load flow is an important tool used by power engineers for planning, to determine the best

operation for a power system and exchange of power between utility companies. In order to have

an efficient operating power system, it is necessary to determine which method is suitable and

efficient for the system’s load flow analysis. This paper presents analysis of the load flow problem

in power system planning studies. The numerical methods: Gauss-Seidel and Newton-Raphson

were compared for a load flow analysis solution. Simulation is carried out using Matlab for test

case of Ayede 330/132kV substation Ibadan Oyo-State. Ayede 330/132KV substation feeds seven

different 132/33KV substations such as Ayede, Ibadan North, Ijebu ode, Iseyin, Iwo, Jericho,

Sagamu substation. The simulation results were compared for number of iteration, computational

time, tolerance value and convergence. The compared results show that Newton-Raphson is the

most reliable method because it has the least number of iteration and converges faster.

Keywords

Load Flow, Bus, Newton-Raphson, Gauss-Seidel, Voltage Magnitude, Voltage Angle, Active

Power, Reactive Power, Iteration, Convergence

1. Introduction

Load-flow analysis is 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, real power

flow, reactive power flow and the power flow in feeder circuits. It determines if system voltage

remain within specified limits under various contingency conditions and whether equipment such

as transformers and conductors are overloaded; used to identify the need for additional generation,

capacitive, or inductive VAR support or the placement of capacitors and/or reactors to maintain

mailto:[email protected]

mailto:[email protected]



ISSN – 2394-0573 All Rights Reserved © 2017 IJEETE 81

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.

Load flow study also consists of system network calculations to determine the performance

of the lines. These calculations are possible only when the real and reactive power flows, bus

voltages and system phase angles are known. In most utility systems, complete system study is

undertaken at regular intervals to complete this analysis, there are methods of mathematical

calculations which consist of numerous steps depending on the size of the system; the node-voltage

method is the most suitable form for many power system analyses. The formulation of the network

equations in the nodal admittance form results in complex linear simultaneous algebraic equations

in terms of node currents. When node currents are specified, the set of linear equations can be

solved for the node voltages. This process is difficult and takes a lot of times to perform by hand.

The objective of this report is to show the comparison between two load flow analysis methods

and determine the best that will help the analysis become easier. The economic load dispatch plays

an important role in the operation of power system and several traditional approaches are normally

used to provide solution to the problems but recently soft computing techniques have received

more attention and are used in a number of successful and practical applications. Iterative

techniques for providing solution to load flow problems are Gauss-Seidel method and Newton-

Raphson method, therefore there is need to determine which of the iterative technique is faster and

more reliable in order to have the best result for load flow analysis.

Moreso, through the load flow studies we can obtain the voltage magnitudes and angles at

each bus in the steady state. This is rather important as the magnitudes of the bus voltages are

required to be held within a specified limit. Once the bus voltage magnitudes and their angles are

computed using the load flow, the real and the reactive power flow through each line can be

computed. Also based on the difference between power flow in sending and receiving ends, the

losses in a particular line can also be computed. Furthermore, from the line flows we can also

determine the overload and loading conditions. The steady state power and reactive power supplied

by a bus in a power network are expressed in terms of non linear algebraic equations. This would

therefore require iterative steps for solving these equations. In this project two of the load flow

methods was used but the major advantages of Newton-Raphson method over Gauss-Seidel




method are: it converges faster, the number of iterations are independent of the size of the system

and computation time per iteration is more unlike Gauss-Seidel method whose rate of convergence

is slower, computation time per iteration is less and the number of iterations required for

convergence increases with size of the buses.

2. Classification of Buses

A bus is defined as a node at which one or many lines, loads and generators are connected.

In a power system each node or bus is associated with four quantities such as magnitude of voltage

(/V/), phase angle of voltage (δ), active or real (P) and reactive power (Q). In load flow problem

two out of these four quantities are specified and the remaining two are required to be determined

by the solution of the equation. Depending on the quantities that have been specified, the buses are

classified into three categories. For load flow studies it is assumed that the loads are constant and

they are defined by their real and reactive power consumption. The main objective of the load flow

is to find the voltage magnitude of each bus and its angle when the power generated and load is

pre-specified. To facilitate this we classify the different buses of the power system.

The following are the classification of Bus:

2.1 Load bus (P-Q Bus)

A load bus is defined as any bus of the system for which the real and reactive power is specified.

Load buses may contain generators with specified real and reactive power outputs, However, it is

often convenient to designate any bus with specified injected complex power as a load complex

power S=P+JQ taken from or injected into the system. Such nodes may also include links to other

systems. At these load nodes, the voltage magnitude (/V/) and phase angle (𝛿) must be calculated.

2.2 Generator Bus (P-V Bus)

Any bus for which the voltage magnitude and the injected real power are specified is classified as

a voltage controlled (P-V) bus. The injected reactive power is a variable (with specified upper and

lower bounds) in power flow analysis and a P-V bus must have a variable source of reactive power

such as a generator.

2.3 Slack (swing) bus

Usually this bus is numbered 1 for the load flow studies. This bus sets the angular reference for all

the other buses. Since it is the angle difference between two voltage sources that indicates the real

and reactive power flow between them, the particular angle of the slack is not important. However

it sets the reference against which angles of all the other bus voltages are measured. For this reason




the angle of this bus is usually chosen as 0°. Furthermore, it is assumed that the voltage of this bus

is known. This node acts as the reference node and is commonly chosen to have a phase angle

𝛿=0°. Generally the following features are given to slack bus. The real and reactive power is

unknown, the bus selected as the slack bus must have a source of both real and reactive power,

since the injected power at this bus must ” swing” to take up the “slack” in the solution. The

behavior of the solution is often influenced by the bus chosen.

3. Formulation of Power Flow Study

According to Gauss-Seidel and Newton-Raphson methods the power flow equations are

non-linear thus cannot be solved analytically. A numerical iterative algorithm is required to solve

such equations. A standard procedure is as follows; create a bus admittance matrix Y bus for the

power system, make an initial estimate for the voltage (both magnitude and phase angle) at each

bus in the system, substitute in the power flow equations and determine the deviations from the

solution, update the estimated voltages based on some commonly known numerical algorithm and

repeat the process until the deviations from the solution are minimal.

3.1 Bus Admittance Matrix

The first step is to number all the nodes of the system from 0 to n. Node 0 is the reference node

(or ground node), replace all generators by equivalent current sources in parallel with admittance

whenever possible and replace all lines, transformers, loads to equivalent admittances whenever

possible. The bus admittance matrix Y is then as follows: sum of admittances connected to node

iiy=i and yij=y ji=-sum of admittances connected from node i to node j. The current vector is next

found from the sources connected to nodes 0 to n. If no source is connected, the injected current

would be 0.The resulting equations are called the node-voltage equations and are given the “bus”

subscript in power studies.

A power flow study is a steady-state analysis whose target is to determine the voltages,

currents, real and reactive power flows in a system under a given load conditions. The basic

equation for power-flow analysis is derived from the nodal analysis equations for the power

system:

𝐼 = 𝑌𝑉 (1)

Where, 𝐼 is the bus current, 𝑌 is the bus admittance matrix and 𝑉 is the vector of bus voltages.




For example, for a 3-bus system,

[𝑌11 𝑌12 𝑌13

𝑌21 𝑌22 𝑌23

𝑌31 𝑌32 𝑌33

] [𝑉1

𝑉2

𝑉3

] = [𝐼1

𝐼2

𝐼3

] (2)

Where, 𝑌𝑖𝑗 are the elements of the bus admittance matrix, 𝑉𝑖 are the bus voltages, and 𝐼𝑙 are the

currents injected at each node. The node equation at bus i can be written as

𝐼𝑖 = ∑ 𝑌𝑖𝑗𝑉𝑗

𝑛

𝑗=1

(3)

The relationship between real and reactive power supplied to the system at bus i and the current

injected into the system at that bus is:

𝑆𝑖 = 𝑉𝑖𝐼𝑖∗ = 𝑃𝑖 + 𝑗𝑄𝑖 (4)

where,𝑉𝑖 is the voltage at the i-th bus, 𝐼𝑖∗ is the complex conjugate of the current injected at the i-th

bus,𝑃𝑖 and 𝑄𝑖 are real and reactive powers at the i-th bus.

Letting 𝑌𝑖𝑗 = 𝑌𝑖𝑗∠𝜃𝑖𝑗 𝑎𝑛𝑑 𝑉𝑖 = 𝑉𝑖∠𝛿𝑖, converting to their polar form with 𝜃𝑖𝑗 and 𝛿𝑖 represent

the admittance and voltage angle. It is more convenient working with 𝐼𝑖 than 𝐼𝑖∗, Eq. (4) can be re-

written as follow:

𝑉𝑖∗𝐼𝑖 = 𝑃𝑖 − 𝑗𝑄𝑖 (5)

Substituting Eq. (2) for 𝐼𝑖 in Eq. (4), then, Eq. (5) is written as follow;

𝑃𝑖 − 𝑗𝑄𝑖 = ∑|𝑌𝑖𝑗|

𝑛

𝑗=1

|𝑉𝑖||𝑉𝑗|∠(𝜃𝑖𝑗 + 𝛿𝑗 + 𝛿𝑖) (6)

Therefore, by separating the real and reactive powers,

𝑃𝑖 = ∑|𝑌𝑖𝑗|

𝑛

𝑗=1

|𝑉𝑖||𝑉𝑗|𝑐𝑜𝑠(𝜃𝑖𝑗 + 𝛿𝑗 + 𝛿𝑖) (7)




𝑄𝑖 = − ∑|𝑌𝑖𝑗|

𝑛

𝑗=1

|𝑉𝑖||𝑉𝑗|sin (𝜃𝑖𝑗 + 𝛿𝑗 − 𝛿𝑖) (8)

There are 4 variables that are associated with each bus: P, Q, V, δ. Meanwhile, there are two power

flow equations associated with each bus. In a power flow study, two of the four variables are

defined and the other two are unknown. That way, we have the same number of equations as the

number of unknown. The known and unknown variables depend on the type of bus.

From (Saadat, 2002) equation (7) and (8) constitute a set of nonlinear algebraic equations in terms of the

independent variables, voltage magnitude in per unit, and phase angle in radians. We have two equations

for each load bus, which is given by (7) and (8) and one equation for each voltage controlled bus, which is

(8). The Jacobian matrix gives the linearized relationship between small changes in voltage angle ∆𝜕𝑖(𝑘)

and voltage magnitude ∆|𝑉𝑖(𝑘)

| with the small changes in real and reactive power ∆|𝑃𝑖(𝑘)

| and∆|𝑄𝑖(𝑘)

|.

Element of the Jacobian matrix are the partial derivatives of (7) and (8) evaluated at ∆𝜕𝑖(𝑘)

and∆|𝑉𝑖(𝑘)

|. In

a short form, it can be written as it can be written as

[∆𝑃∆𝑄

]=[𝐽1 𝐽2

𝐽3 𝐽4] [

∆𝛿∆|𝑉|

] (9)

For voltage-controlled buses, the voltage magnitude is known.

The diagonal and the off-diagonal element and of 𝐽1 are

𝜕𝑃𝑖

𝜕𝛿𝑖=∑ |𝑉𝑖||𝑗≠𝑖 𝑉𝑗||𝑌𝑖𝑗|𝑆𝑖𝑛(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) (10)

𝜕𝑃𝑖

𝜕𝛿𝑗=−|𝑉𝑖||𝑉𝑗||𝑌𝑖𝑗|𝑆𝑖𝑛(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) 𝑗 ≠ 𝑖 (11)


𝜕𝑃𝑖

𝜕|𝑉𝑖|=2 |𝑉𝑖||𝑌𝑖𝑗|𝐶𝑜𝑠𝜃𝑖𝑖 + ∑ |𝑉𝑗𝑗≠𝑖 ||𝑌𝑖𝑗|𝐶𝑜𝑠(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) (12)

𝜕𝑃𝑖

𝜕|𝑉𝑗 |=|𝑉𝑗||𝑌𝑖𝑗|𝐶𝑜𝑠(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) 𝑗 ≠ 𝑖 (13)


𝜕𝑄𝑖

𝜕𝛿𝑖=∑ |𝑉𝑖||𝑗≠𝑖 𝑉𝑗||𝑌𝑖𝑗|𝐶𝑜𝑠(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) (14)

𝜕𝑄𝑖

𝜕𝛿𝑗=−|𝑉𝑖||𝑉𝑗||𝑌𝑖𝑗|𝐶𝑜𝑠(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) 𝑗 ≠ 𝑖 (15)





𝜕𝑄𝑖

𝜕|𝑉𝑖|=−2 |𝑉𝑖||𝑌𝑖𝑗|𝑆𝑖𝑛𝜃𝑖𝑖 − ∑ |𝑉𝑗𝑗≠𝑖 ||𝑌𝑖𝑗|𝑆𝑖𝑛(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) (16)

𝜕𝑄𝑖

𝜕|𝑉𝑗 |=−|𝑉𝑗||𝑌𝑖𝑗|𝑆𝑖𝑛(𝜃𝑖𝑗 − 𝛿𝑖 + 𝛿𝑗) 𝑗 ≠ 𝑖 (17)

The term ∆|𝑃𝑖(𝑘)

| and ∆|𝑄𝑖(𝑘)

| are the difference between the scheduled and the calculated values,

known as the power residuals, given by

∆𝑃𝑖(𝑘)

= 𝑃𝑖𝑠𝑐ℎ − 𝑃𝑖

(𝑘) (18)

∆𝑄𝑖(𝑘)

= 𝑄𝑖𝑠𝑐ℎ − 𝑄𝑖

(𝑘) (19)

The new estimates for bus voltages are

𝛿𝑖(𝑘+1)

= 𝛿𝑖𝑠𝑐ℎ + ∆𝛿𝑖

(𝑘) (20)

|∆𝑉𝑖(𝑘+1)

|= |𝑉𝑖(𝑘)

| + ∆|𝑉𝑖(𝑘)

| (21)

The procedure for power flow solution by the Newton-Raphson method is as follows: For load

buses, where 𝑃𝑖(𝑠𝑐ℎ)

and 𝑄𝑖(𝑠𝑐ℎ)

are specified, voltage magnitudes and phase angles are set equal to

the slack bus values, or 1.0 and 0.0, i.e., |𝑉𝑖(0)

|=1.0 and 𝛿𝑖(0)

=0.0. For voltage regulated buses,

where |𝑉𝑖| and 𝑃𝑖𝑠𝑐ℎ are specified, phase angles are set to the slack bus angle or 0, i.e., 𝛿𝑖

(0)=0.0.

For load buses, 𝑃𝑖(𝑠𝑐ℎ)

and 𝑄𝑖(𝑠𝑐ℎ)

are calculated from (7) and (8) respectively and ∆𝑃𝑖(𝑘)

and ∆𝑄𝑖(𝑘)

are calculated from (18) and (19) respectively. For voltage-controlled buses, 𝑃𝑖(𝑘)

and ∆𝑃𝑖(𝑘)

are

calculated form (7) and (18) respectively. The element of the Jacobian matrix (𝐽1, 𝐽2 , 𝐽3, 𝑎𝑛𝑑 𝐽4)

are calculated from (10) and (18). The linear simultaneous equation (10) is solved directly by

optimally ordered triangular factorization and Gaussian elimination. The new voltage magnitude

and phase angles are computed from (20) and (21).The process is continued until the residual ∆𝑃𝑖(𝑘)

and ∆𝑄𝑖(𝑘)

are less than the specified accuracy i.e.

|∆𝑃𝑖(𝑘)

| ≤ 𝜖 (22)

|∆𝑄𝑖(𝑘)

| ≤ 𝜖 (23)

In order to perform load flow, using Gauss-Seidel and Newton-Raphson method as describe above

we have to obtain the resistance and impedance of each 132kV transmission lines as shown in

Figure 1




Figure

1: Single line diagram for a three phase transmission line

In Figure 1, 1 is the slack while 2, 3, 4, 5, 6, 7, 8 are the load buses. The geometric mean distance

is given as

𝐷𝐺𝑀𝐷 = √𝑥𝑦𝑧 3 (24)

Figure 2: Single line diagram of a three phase line

The reactance per phase per kilometer length is

𝑥𝑂 = 0.144 log [𝐷𝐺𝑀𝐷

𝑟] + 0.016 (25)

With r given as the radius of the conductor. The cross sectional area of the conductor is 250mm2

and the radius is gotten as

𝑟 = √𝐴

3.142 (26)

The resistance R of the line is

2 3

1

4 5 6 A

YE

DE

IB

AD

AN

IJ

EB

U-O

DE

IS

EY

IN

IWO

330kV bus

Supply

Transmission

line

Bus bar

KEY

7 8

JER

ICH

O

SH

AG

AM

U

Z

Y

X

For 132kV transmission line

X=1.7m

Y=1.7m

Z=3.4m




𝑅 =𝜌𝐿

𝐴 (27)

where 𝜌 = 3.26𝑥10−8 Ω

𝑚 𝑎𝑛𝑑 𝐿 𝑎𝑟𝑒 the resistivity and distance of supply. The impedance of

each line shown in Figure 3.1 is

𝑍𝑏𝑎𝑠𝑒 =[𝑉𝑏𝑎𝑠𝑒]2

𝑀𝑉𝐴𝑏𝑎𝑠𝑒 (28)

𝑍𝑏𝑎𝑠𝑒 =[132000]2

100000000= 174.24 Ω (29)

𝑍𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑅 + 𝑗𝑥 𝑂Ω (30)

𝑍𝑝𝑢 =𝑍𝑎𝑐𝑡𝑢𝑎𝑙

𝑍𝑏𝑎𝑠𝑒 (31)

The parameter from Table 1 and Table 2 and then imputed in the Gauss-Seidel and Newton-

Raphson Matlab code to compute the load flow as required.

4. Simulation Results

The simulation for Gauss-Seidel and Newton-Raphson method is carried out using Matlab for test

case Ayede 330/132kV substation. The base mva, selected value for iteration (tolerance) and

maximum numbers of iterations is specified. The simulation results are shown in Figure 3, Figure

4 for Gauss-Seidel and Newton- Raphson method respectively. The bus system consists of Bus 1

which acts as a slack bus. It consists of 7 load buses which are connected to load.




Figure 3: Simulation result for Ayede 330/132kV using Gauss-Seidel method.

Figure 4: Simulation result for Ayede 330/132kV using Newton-Raphson method




Ayede 330/132kV consist of eight line data as represented in Table 2 which shows the

values for resistance, reactance and half susceptance in per unit for the transmission line connected

together. It also shows the tap setting values for transformers and the position of the transformers

on the transmission line. The information is used to form the admittance bus matrix.

Table 3 represents the line flow and line losses for each of the Ayede 330/132kV bus

system. The line losses are compared for the two iterative techniques: Gauss-Seidel and Newton-

Raphson method while Gauss-Seidel have the highest total losses of 5.277 MW, 14.518 Mvar and

Newton-Raphson have the least losses of 5.271 MW, 14.503 Mvar.

Table 1: Load Data Of Ayede Bus System.

Bus Type of Bus/ Name of feeder

Voltage Load Generation

/V/(P,U) δ(θ) P(MW) Q(Mvar) P(MW) Q(Mvar)

1 Slack 1.0000 0 0 0

2 PQ/Ayede 1.0000 0 128 96

3 PQ/Ibadan-North 1.0000 0 48 36

4 PQ/Ijebu-Ode 1.0000 0 48 36

5 PQ/Iseyin 1.0000 0 36 27

6 PQ/Iwo 1.0000 0 32 24

7 PQ/Jericho 1.0000 0 68 51

8 PQ/Shagamu 1.0000 0 48 36

Table 2: Line data of Ayede 330/132kV bus system

Bus No Bus No R,pu X, pu 0.5B,pu Transformer

tap

1 2 0.0004865 0.0013385 0 1

1 3 0.007930 0.02183 0 1

1 4 0.03832 0.10543 0 1

1 5 0.05239 0.1441 0 1

1 6 0.02919 0.0803 0 1

1 7 0.002694 0.0074132 0 1

1 8 0.047448 0.130555 0 1




Table 3: Line flow and losses comparing for Ayede 330/132kV

From

Bus

To

Bus

Newton-Raphson

Method

Gauss-Seidel Method

P Q Lines loss P Q Lines loss

MW Mvar MW Mvar MW Mvar MW Mvar

1 2 413.271 320.503 0.000 0.000 412.976 320.703 0.000 0.000

1 3 128.113 96.312 0.113 0.312 128.113 96.312 0.113 0.312

1 4 48.265 36.728 0.265 0.728 48.265 36.728 0.265 0.728

1 5 49.400 39.852 1.400 3.852 49.408 39.847 1.400 3.853

1 6 37.080 29.971 1.080 2.971 37.088 29.966 1.080 2.972

1 7 32.447 25.230 0.447 1.230 32.447 25.230 0.447 1.230

1 8 68.178 51.491 0.178 0.491 68.178 51.491 0.178 0.491

1 9 49.787 40.918 1.787 4.918 50.054 40.738 1.792 4.932

5. Discussion

5.1 Tolerance

The selected tolerance iteration value used for the simulation is shown in Table 5. This is used to

determine how accurate a solution will be. Thus, using a high tolerance value for a simulation

increases the accuracy of the solution whereas when a low tolerance value is used, it reduces the

accuracy of the solution and number of iterations. The selected tolerance value used for the

simulation is 0.001 and 0.1. Thus the 0.001 did not converge with the Gauss-Seidel method but

converge at 0.1 while the Newton-Raphson method converges at the tolerance value of 0.001 and

0.1.

5.2 Iteration number

Table 5 and Table 6 show the number of iterations for the power flow solution using selected

iteration value of 0.001 and 0.1 respectively to converge for the two load flow methods. Gauss-

Seidel Method has the highest number of iterations before it converges. The number of iteration

increases as the number of buses in the system increases. Newton-Raphson has the least number




of iteration to converge. For the Gauss-Seidel method, the load flow solution did not converge

using 0.001. Then another selected value of 0.1 was chosen for the iteration.

5.3. Computing time

The computation time for load flow solutions using selected iteration value of 0.001 is shown in

Table 8 and Table 9 respectively. Newton-Raphson has same computation time as the number of

buses increases. Newton-Raphson has more computational time compared among the three

methods. Gauss-Seidel has the least computation.

Table 4: Comparison of tolerance value

Test System Gauss-Seidel Newton-Raphson

Ayede 330/132kV 0.001/0.1 0.001/0.1

Table 5: Comparison of iteration number using selected value of 0.001


Ayede 330/132kV 101 4

Table 6: Comparison of iteration number using selected value of 0.1


Ayede 330/132kV 21 3

Table 7: Comparison of computing time using selected value of 0.001


Ayede 330/132kV 2.08 seconds 0.0360 seconds




Table 8: Comparison of computing time using selected iteration value of 0.1


Ayede 330/132kV 0.048 seconds 0.0355 seconds

5.4. Convergence

Convergence is used to determine how fast a power flow reaches its solution. The convergence

rate for Gauss-Seidel is slow compared to the other. Newton-Raphson has the fastest rate of

convergence among the two numerical methods.

6. CONCLUSIONS

All the simulations were carried out using Matlab and implemented for Ayede 330/132 kV bus

test cases for Gauss-Seidel and Newton-Raphson. In the load flow analysis methods simulated, the

tolerance values used for simulations are 0.001 and 0.1 for all the simulation carried out except for

the Gauss-Seidel method which did not converge with the tolerance value 0.001. This explains

why the Gauss-Seidel method is not as accurate as Newton-Raphson method because a lower

tolerance value of 0.1 was used to carry out the simulation.

The time for iteration in Gauss-Seidel is the longest compared to the Newton-Raphson

method . The time for iterations in Gauss-Seidel increases as the number of buses increases. The

Gauss-Seidel method increases in arithmetic progression. Newton-Raphson increases in quadratic

progression. This explains why it takes longer time for Gauss-Seidel to converge. The

computational time for Gauss-Seidel is low compared to Newton-Raphson. Newton-Raphson have

more computational time due to the complexity of the Jacobian matrix for each iteration but still

converges fast enough because less number of iterations are carried out and required.

The results of this paper suggest that the planning of a power system can be carried out by

using Gauss-Seidel method for a small system with less computational complexity due to the good

computational characteristics it exhibited. The effective and most reliable amongst the two load

flow methods is the Newton-Raphson method because it converges fast and is more accurate.

References




(1) Temitope Adefarati, Adedayo Kayode Babarinde, Ayodele Sunday Oluwole and Kehinde

Olusuyi (2014) Reliability Evaluation Of Ayede 330/132kV Substation ISSN: 2277-3754 ISO

9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT)

Volume 4, Issue 4, October 2014.

(2) Adejumobi, I.A., et al. (2014) Numerical Methods in Load Flow Analysis: An Application to

Nigeria Grid System. International Journal of Electrical and Electronics Engineering (IJEEE) 3.

(3) Hadi, S. (2010) Power System Analysis. 3rd Edition, PSA Publishing, North York.

(4) Bhakti, N. and Rajani, N. (2014) Steady State Analysis of IEEE-6 Bus System Using PSAT

Power Tool Box. International Journal of Engineering Science and Innovation Technology

(IJESIT), 3.

(5) Aroop, B., Satyajit, B. and Sanjib, H. (2014) Power Flow Analysis on IEEE 57 bus System

Using Mathlab. International Journal of Engineering Research & Technology (IJERT), 3.

(6) Afolabi, O.A., Ali, W.H., Cofie, P., Fuller, J., Obiomon, P. and Kolawole, E.S. (2015)

Analysis of the Load Flow Problem in Power System Planning Studies. Energy and Power

Engineering, 7, 509-523. http://dx.doi.org/10.4236/epe.2015.710048

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