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The load-flow study in a power system has great importance because it is the
only system which shows the electrical performance and power flow of the
system operating under steady state. The load-flow study also provides the real and
reactive power losses of the system and voltages at different nodes of the system.
An efficient load-flow study plays vital role during planning of the system
and also for the stability analysis of the system. Distribution networks are
weakly meshed structurally but are operated with a radial structure due to its
simplicity in design and cost. On the other hand, the transmission system is loop like
in nature. Distribution networks have high R/X ratio whereas the
transmission networks have high X/R ratio. Hence, the distribution networks are
ill-conditioned in nature. Therefore, the variables for the load-flow analysis of distribution
systems are different from those of transmission systems. The load-flow methods
proposed by researchers (Tinney and Hart, 1967; and Scott and Alasc, 1974) do not
converge for the ill-conditioned networks. The following methods are available in
literature for load-flow analysis of distribution systems. The methods proposed in
Iwamoto and Tamura (1981) and Rajjic and Tamura (1988) are very time consuming
and increase the complexity.
Kersting and Mendive (1976), and Kersting (1984) developed a
load-flow technique for solving radial distribution networks that update voltages and
currents during the backward and forward sweeps with the help of a ladder network
theory. Stevens et al. (1986) showed that the method proposed in Kersting and
Mendive (1976) and Kersting (1984) became the fastest but failed to converge in five
out of 12 cases studied. Shirmohammadi et
al. (1988) developed a method for solving radial distribution networks by applying the direct voltage application of
Kirchoff's laws and presented a branch numbering scheme to increase the
numerical performance of the solution method. They also extended their method for
solving the weakly meshed distribution networks. Baran and Wu (1989a) proposed
the load-flow solution of radial distribution networks by iterative solution of
three fundamental equations representing the real power, reactive power and
voltage magnitude. Chiang and Baran (1990) showed the uniqueness of load-flow
solution for radial distribution networks. Renato (1990) proposed one method for
obtaining load-flow solution of radial distribution networks by computing the
electrical equivalent for each node, summing all the loads of the network fed through
the node including losses. Then, starting from the source node, the voltage of
every receiving end node was computed. Chiang (1991) showed three different
algorithms for solving radial distribution networks based on the method of Baran and
Wu (1989a). Goswami and Basu (1991) presented an approximate method
using sequential numbering scheme for solving radial and meshed distribution
networks with a condition that any node in the network could not be the junction of
more than three branches i.e., one incoming and two outgoing. Jasmon and Lee
(1991) presented a load-flow method for obtaining the load-flow solution
of radial distribution networks with the help of three fundamental
equations representing the real power, reactive power and voltage magnitude that had
been proposed by Baran and Wu (1989a). Das et
al. (1994) proposed a load-flow method using sequential numbering scheme which needs a number of codes for the
laterals and sub laterals. If another sub lateral exists for the sub lateral, this
method needs more data preparation and hence becomes more complicated.
For a large system, this method increases the complexity of computation.
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