Load flow and system reliability studies are frequently performed by the power system
planning, operation and maintenance engineers. The power system is represented by a
set of nonlinear algebraic equations to solve these equations. Many algorithms and methods
have been presented by researchers in the past six decades (Brown and Tinney, 1957;
Glimn and Stagg, 1957; Wu 1977; Chien and Kuh, 1977; Abe et al., 1978; Rao et al.,
1984; Amereongan et al., 1989; Grainger and Stevenson, 1994; and Ahsan and Jalil,
2005). Mathematically, this involves the solution of a set of nonlinear algebraic equations
(Stagg and El Abiad, 1968). A vast literature is available in this area, but only a few
references are considered here (Ward et al., 1956; Brown et al., 1957; Glimn et al.,
1957; Tinney et al., 1967; Stagg et al., 1968; Misra, 1970; Stott et al., 1974; Abe et al.,
1977; Chien et al., 1977; Johnson, 1977; Wu, 1977; Abe et al., 1978; Rao, 1981; Rao
et al., 1981 and 1984, Ameraongan, 1989; Grainger et al., 1994; Prasad et al., 2004;
Ashan et al., 2005; and Sharma et al., 2006). The load flow calculations are extensively
used to solve the large power system problems. These are also used to solve multiple
cases for the purposes such as outage security assessment, optimization and system
reliability. The earliest load flow solution using digital computers appeared in 1956 (Ward
and Hale, 1956). It is a well-known fact that the Newton-Raphson method is one of the most powerful methods having good quadratic convergence property (Tinney and Hart,
1967). Later, the fast decoupled load flow method was proposed by Stott and Alsac
(1974) in the year 1974. The fast decoupled load flow method has gained considerable popularity and acceptance for the solution of load flow problems since 1974 and is popular
even today due to its simplicity, solution speed and storage capacity. It is observed that
this method also has the convergence problem in certain situations like: (1) presence of
lines having the large R/X ratios; (2) presence of lines having capacitive series branches;
and (3) heavy loading of the system and on sudden load rejection. It is also well-known
that load flow equations are the set of nonlinear simultaneous equations and that the
function has no unique solution from the nonlinear equations theory.
On the other hand, it may be possible that the solution is sometimes found to be
extraneous or false, as showen by Johnson (1977). He also showed that false or
extraneous solutions may occur when the power network or power system problems
are being studied for heavily loaded condition or for the system with high voltage
transmission lines. The false load flow solutions may also occur for a power system
having the generator with capacitive apparent system impedance. Abe and Isono (1977)
have also showen that careless choice of initial solution guess point may also be the
cause of convergence problem; it may sometimes provide an undesired solution. Rao
(1981) have also shown the possibility of such solutions and their existence in the power
system. The N-R method always converges to the desired solution if the solution exists
within the region of the initial guess solution. When the initial guess point is chosen far
from the solution, it may not converge to the desired solution. It is stated in literature
(Rao et al., 1981) that load flow equations do not necessarily guarantee the correct or
desired solution. Thus there is no reliable method available which may provide the
solution or multiple solutions with the same initial and arbitrarily chosen point. The
method capable of increasing the load flow system reliability is also not yet reported in
literature. Thus following Misra (1970), the important aspect, i.e., standby redundancy,
is used. |
