1. RAJ KUMAR GOEL INSTITUTE OF TECHNOLOGY, GHAZIABAD
ELECTRICAL & ELECTRONICS ENGG.
SYNOPSIS ON
LOAD FLOW ANALYSIS USING NEWTON- RAPHSON
METHOD
GROUP
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MUDIT JAIN
PROJE CT GUIDE: PROJECT COORDINATOR
Mr. Varun Singhal Mrs. Kiran Srivastava
Associate Professor
HEAD OF DEPARTMENT
DR. VINAY KAKKAR
(DEPT. OF ELECTRICAL & ELECTRONICS ENGG. )

2. OBJECTIVES:
 To demonstrate load flow concepts.
 To study system performance under different operating conditions.
 To experience the real feel of power system operation .
BACKGROUND:
LOAD FLOW ANALYSIS is probably the most important of all network calculations since it
concerns the network performance in its normal operating conditions. It is performed to
investigate the magnitude and phase angle of the voltage at each bus and the real and reactive
power flows in the system components.
Load flow analysis has a great importance in future expansion planning, in stability studies and
in determining the best economical operation for existing systems. Also load flow results are
very valuable for setting the proper protection devices to insure the security of the system. In
order to perform a load flow study, full data must be provided about the studied system, such as
connection diagram, parameters of transformers and lines, rated values of each equipment, and
the assumed values of real and reactive power for each load.
We should be able to analyze the performance of power systems both in normal operating
conditions and under fault (short-circuit) condition. The analysis in normal steady-state operation
is called a power-flow study (load-flow study) and it targets on determining the voltages,
currents, and real and reactive power flows in a system under a given load conditions.
The purpose of power flow studies is to plan ahead and account for various hypothetical
situations. For instance, what if a transmission line within the power system properly supplying
loads must be taken off line for maintenance. Can the remaining lines in the system handle the
required loads without exceeding their rated parameters?
ADVANTAGES OF LOAD-FLOW STUDIES:
 Load flow or power flow is a solution for the power system under STATIC
CONDITIONS OF OPERATION.
 Load flow is easy to determine –
Line flow
Bus voltage
System voltage of profile
Effect of changes in circuit configuration and incorporating new circuits on system
loading.
The effect of temporary loss of transmission capacity or generation on system
loading.
Effect of In-phase and boost voltage in system loading.
Economic system operation
Transmission line loss minimization

3. Transformer tap settings for economic operation
Possible improvements to an existing system by change of conductor size and system
voltages.
 It is a starting point for many other studies like short-circuit and transient stability.
A load flow solution of the power system requires mainly the following stages:
 Network Modelling Stage
 Mathematical modeling stage
 Solution stage.
BUS CLASSIFICATION :
Each bus in the system has four variables: voltage magnitude, voltage angle, real power and
reactive power. During the operation of the power system, each bus has two known variables and
two unknowns. Generally, the bus must be classified as one of the following bus types:
1.Slack or Swing Bus
This bus is considered as the REFERENCE BUS. It must be connected to a generator of high
rating relative to the other generators. During the operation, the voltage of this bus is always
specified and remains constant in magnitude and angle. In addition to the generation assigned to
it according to economic operation, this bus is responsible for supplying the losses of the system.
2. Generator or Voltage Controlled Bus
During the operation the voltage magnitude at this the bus is kept constant. Also, the active
power supplied is kept constant at the value that satisfies the economic operation of the system.
Most probably, this bus is connected to a generator where the voltage is controlled using the
excitation and the power is controlled using the prime mover control (as you have studied in the
last experiment). Sometimes, this bus is connected to a VAR device where the voltage can be
controlled by varying the value of the injected VAR to the bus.
3. Load bus
This bus is not connected to a generator so that neither its voltage nor its real power can be
controlled. On the other hand, the load connected to this bus will change the active and reactive
power at the bus in a random manner. To solve the load flow problem we have to assume the
complex power value (real and reactive) at this bus.

4. BASIC TECHNIQUES FOR POWER-FLOW STUDIES:
A power-flow study (load-flow study) is an analysis of the voltages, currents, and power flows
in a power system under steady-state conditions. In such a study, we make an assumption about
either a voltage at a bus or the power being supplied to the bus for each bus in the power system
and then determine the magnitude and phase angles of the bus voltages, line currents, etc. that
would result from the assumed combination of voltages and power flows.
The simplest way to perform power-flow calculations is by iteration:
1. Create a bus admittance matrix Ybus for the power system;
2. Make an initial estimate for the voltages at each bus in the system;
3. Update the voltage estimate for each bus (one at a time), based on the estimates for the
voltages and power flows at every other bus and the values of the bus admittance matrix:
since the voltage at a given bus depends on the voltages at all of the other busses in the
system (which are just estimates), the updated voltage will not be correct. However, it
will usually be closer to the answer than the original guess.
4. Repeat this process to make the voltages at each bus approaching the correct answers
closer and closer…
CONSRTUCTING YBUS FOR POWER FLOW SOLUTION :
The most common approach to power-flow analysis is based on the bus admittance matrix Ybus.
However, this matrix is slightly different from the one studied previously since the internal
impedances of generators and loads connected to the system are not included in Ybus. Instead,
they are accounted for as specified real and reactive powers input and output from the buses.
Power-flow analysis equations :
The basic equation for power-flow analysis is derived from the nodal analysis equations for the
power system:
Ybus V = I ------------------ (1)
For a four- bus power system, it becomes
Y11 Y12 Y13 Y14 V1 I1
Y21 Y22 Y23 Y24 V2 I2
=
Y31 Y32 Y33 Y34 V3 I3
Y41 Y42 Y43 Y44 V4 I4

5. where Yij are the elements of the bus admittance matrix, Vi are the bus voltages, and Ii are the
currents injected at each node. For bus 2 in this system, this equation reduces to
Y21 V1 +Y 22 V2 +Y 23 V3 +Y24 V4 = I2 ----------------------( 2)
The real and reactive power at bus i is given by :
The current can be expressed in terms of the active and the reactive power at bus i as:
Separating the real and imaginary parts:
These are the steady-state power flow equations expressed in polar form.

6. THE INFORMATION DERIVED FROM POWER FLOW
STUDIES :
Also, comparing the real and reactive power flows at either end of the transmission line, we can
determine the real and reactive power losses on each line.
Power-flow studies are usually started from analysis of the power system in its normal operating
conditions, called the base case. Then, various (increased) load conditions may be projected to
localize possible problem spots (overloads). By adding transmission lines to the system, a new
configuration resolving the problem may be found. This estimated models can be used for
planning.
Another reason for power-flow studies is modeling possible failures of particular lines and
generators to see whether the remaining components can handle the loads.
Finally, it is possible to determine more efficient power utilization by redistributing generation
from one locations to other. This variety of power-flow studies is called ECONOMIC
DISPATCH.
TECHNIQUES OF SOLUTION :
Because of the nonlinearity and the difficulty involved in the analytical expressions for the above
power flow equations, numerical iterative techniques must be used such as:
1. Gauss-Seidel method (G-S).
2. Newton-Raphson method (N-R).
3. Fast decoupled method (F-D).
ADVANTAGES OF NEWTON-RAPHSON METHOD:
Over the past few years, developments have been made in finding digital computer solutions for
power-system load flows. This involves increasing the reliability and the speed of convergence
of the numerical-solution techniques. In routine use, even few failures to give first-time
convergence for physically feasible problems can be uneconomical. Hence, the Newton-Raphson
(NR) approach is the most preferred general method.
The Newton-Raphson approach is the most preferred load flow method because of its various
advantages.
 It has powerful convergence characteristics compared to alternative processes.
 Considerably low computing times are achieved when the sparse network equations are
solved by the technique of sparsity-programmed ordered elimination .
 The NR approach is particularly useful for large networks as computer storage
requirements are moderate and increase with problem size almost linearly.

7.  The method is very sensitive to a good starting condition. The use of a suitable starting
condition reduces the computation time remarkably, as well as ensures the convergence.
 No acceleration factors have to be determined, the choice of slack bus is rarely critical,
and network modifications require quite less computing effort.
 The NR method has great generality and flexibility, hence enabling a wide range of
representational requirements to be included easily and efficiently, such as on load tap
changing and phase-shifting devices, area interchanges, functional loads and remote
voltage control.
 The NR load flow is central to many recently developed methods for the optimization of
power system operation, sensitivity analysis, system-state estimation, linear-network
modelling, security evaluation and transient-stability analysis, and it is well suited to online
computation .
Characterizing the in numeral advantages and the future prospects we adopted the NEWTON
RAPHSON METHOD for load flow analysis computations.

8. REFERENCES :
I. International journal of research in IT and Management.
II. Power System Analysis, Hadi saadat, McGraw Hill International editions.
III. Kundur, P., Power System Stability and Control, McGraw-Hill, 1994
IV. Load flows, Chapter 18,Bus classification, Comparison of solution methods, N-R
method–Electrical Power system by C.L.WADHWA.