15-10-2012, 10:36 AM
LOAD FLOW SOLUTION OF UNBALANCED RADIAL DISTRIBUTION SYSTEMS
[attachment=36372]
ABSTRACT
This paper presents a simple three phase load flow method to solve three-phase unbalanced radial
distribution system (RDS). It solves a simple algebraic recursive expression of voltage magnitude, and all
the data are stored in vector form. The algorithm uses basic principles of circuit theory and can be easily
understood. Mutual coupling between the phases has been included in the mathematical model. The
proposed algorithm has been tested with several unbalanced distribution networks and the result of an
unbalanced RDS is presented in the article. The application of the proposed method is also extended to find
optimum location for reactive power compensation and network reconfiguration for planning and day-today
operation of distribution networks.
INTRODUCTION
Load flow technique is very important
tool for analysis of power systems and used in
operational as well as planning stages. Certain
applications, particularly in distribution
automation and optimization require repeated
load flow solutions. As the power distribution
networks become more and more complex, there
is a higher demand for efficient and reliable
system operation. Consequently, the most
important system analysis tool, load flow studies,
must have the capability to handle various
system configurations with adequate accuracy
and speed.
In many cases, it is observed that the
radial distribution systems are unbalanced
because of single-phase, two-phase and threephase
loads. Thus, load flow solution for
unbalanced case and, hence special treatment is
required for solving such networks.
Due to the high R/X ratios and
unbalanced operation in distribution systems, the
Newton-Raphson and ordinary Fast Decoupled
Load Flow method may provide inaccurate
results and may not be converged. Therefore,
conventional load flow methods cannot be
directly applied to distribution systems. In many
cases, the radial distribution systems include
untransposed lines which are unbalanced because
of single phase, two phase and three phase loads.
Thus, load flow analysis of balanced radial
distribution systems [1-3] will be inefficient to
solve the unbalanced cases and the distribution
systems need to be analyzed on a three phase
basis instead of single phase basis.
DISTRIBUTED LOADS
In the unbalanced distribution system,
loads can be uniformly distributed long a line.
When the loads are uniformly distributed, it is
not necessary to model each and every load in
order to determine the voltage drop from the
source end to the last loads.
From D. Shirmohammadi [19], the total
distributed load on each phase of a line section is
lumped half-half at the line section's of two end
buses. So now the load is at bus p and bus q can
be model as spot loads shown in the Fig. 4.
Depending on the spot load type use the eqns. (7)
and (8) to calculate the load current at respective
p and q buses.
CONCLUSIONS
In this paper, a simple and efficient computer
algorithm has been presented to solve
unbalanced radial distribution networks. The
proposed method has good convergence property
for any practical distribution networks with
practical R/X ratio. Computationally, this method
is extremely efficient, as it solves simple
algebraic recursive equations for voltage
phasors. Another advantage of the proposed
method is all the data is stored in vector form,
thus saving enormous amount of computer
memory.
[attachment=36372]
ABSTRACT
This paper presents a simple three phase load flow method to solve three-phase unbalanced radial
distribution system (RDS). It solves a simple algebraic recursive expression of voltage magnitude, and all
the data are stored in vector form. The algorithm uses basic principles of circuit theory and can be easily
understood. Mutual coupling between the phases has been included in the mathematical model. The
proposed algorithm has been tested with several unbalanced distribution networks and the result of an
unbalanced RDS is presented in the article. The application of the proposed method is also extended to find
optimum location for reactive power compensation and network reconfiguration for planning and day-today
operation of distribution networks.
INTRODUCTION
Load flow technique is very important
tool for analysis of power systems and used in
operational as well as planning stages. Certain
applications, particularly in distribution
automation and optimization require repeated
load flow solutions. As the power distribution
networks become more and more complex, there
is a higher demand for efficient and reliable
system operation. Consequently, the most
important system analysis tool, load flow studies,
must have the capability to handle various
system configurations with adequate accuracy
and speed.
In many cases, it is observed that the
radial distribution systems are unbalanced
because of single-phase, two-phase and threephase
loads. Thus, load flow solution for
unbalanced case and, hence special treatment is
required for solving such networks.
Due to the high R/X ratios and
unbalanced operation in distribution systems, the
Newton-Raphson and ordinary Fast Decoupled
Load Flow method may provide inaccurate
results and may not be converged. Therefore,
conventional load flow methods cannot be
directly applied to distribution systems. In many
cases, the radial distribution systems include
untransposed lines which are unbalanced because
of single phase, two phase and three phase loads.
Thus, load flow analysis of balanced radial
distribution systems [1-3] will be inefficient to
solve the unbalanced cases and the distribution
systems need to be analyzed on a three phase
basis instead of single phase basis.
DISTRIBUTED LOADS
In the unbalanced distribution system,
loads can be uniformly distributed long a line.
When the loads are uniformly distributed, it is
not necessary to model each and every load in
order to determine the voltage drop from the
source end to the last loads.
From D. Shirmohammadi [19], the total
distributed load on each phase of a line section is
lumped half-half at the line section's of two end
buses. So now the load is at bus p and bus q can
be model as spot loads shown in the Fig. 4.
Depending on the spot load type use the eqns. (7)
and (8) to calculate the load current at respective
p and q buses.
CONCLUSIONS
In this paper, a simple and efficient computer
algorithm has been presented to solve
unbalanced radial distribution networks. The
proposed method has good convergence property
for any practical distribution networks with
practical R/X ratio. Computationally, this method
is extremely efficient, as it solves simple
algebraic recursive equations for voltage
phasors. Another advantage of the proposed
method is all the data is stored in vector form,
thus saving enormous amount of computer
memory.