Application of Modified Subgradient Algorithm
Based on Feasible Values to Security Constrained
Non-Convex Economic Dispatch Problems with
Prohibited Zones
Salih Fadıl1
Department of Electrical and Electronics Engineering
Eskisehir Osmangazi University, 26480 Eskisehir TURKEY.
E-mail: sfadil@ogu.edu.tr, Phone: +90 (222) 239 2840 x 3264, Fax: +90 (222)
221 39 18
Burak Urazel
Department of Electrical and Electronics Engineering
Eskisehir Osmangazi University, 26480 Eskisehir TURKEY.
E-mail: burazel@ogu.edu.tr
Bünyamin Tamyürek
Department of Electrical and Electronics Engineering
Eskisehir Osmangazi University, 26480 Eskisehir TURKEY.
E-mail: btamyurek@ogu.edu.tr
Abstract
Objective
The non-convex power dispatch problems considered in recent literature
are mostly solved via dispatching techniques that employ evolutionary
methods and use simplified models of power systems. Although the
constraints associated with the active generations of the units are
modeled in a detailed manner, the other constraints of the exact
models of the power systems such as the voltage magnitude, transmission
line loadability, and so on are not employed in the optimization
models used by those methods. If the exact models of the power systems
were used in those dispatch techniques, the solution times would
1
Corresponding author
increase drastically. This is because a power flow calculation is required
for each possible solution in the solution population. Therefore, the
objective of this research is to introduce a deterministic dispatch
technique which can solve the non-convex dispatch problems in less time
and importantly using the exact models of the power systems. The
significant saving in the solution time is due to the elimination of the
power flow calculations from the method except at the initial step.
Method
A security constrained power dispatch problem with non-convex total
cost rate function for a lossy electric power system is formulated and
solved using an iterative solution method based on the modified
subgradient algorithm operating on feasible values (F-MSG). Since all
equality and inequality constraints and the cost function in the
proposed nonlinear optimization model are written in terms of the bus
voltage magnitudes, the phase angles, the off-nominal tap settings, and
the susceptance values of static-var (SVAR) systems, they can be taken as
independent (decision) variables. Moreover, the actual power system loss
is included in the solution of the optimization model since the load flow
equations are inserted into the model as the equality constraints. In
addition, the constraints of the unit generations, the transmission line
capacities, the bus voltage magnitudes, the off-nominal tap settings,
and
the
SVAR
systems
susceptance
values
are
inserted
into
the
optimization problem as the inequality constraints. The prohibited
generation zones are taken into consideration when writing the active
power generation inequality constraints of the units. Since the modified
subgradient algorithm operating on feasible values requires that all
inequality constraints should be expressed in equality constraint form,
all inequality constraints in the optimization model are converted into
corresponding equality constraints by a method that does not add any
extra independent variable into the model. It is therefore the solution
time of the proposed dispatch technique is reduced further.
Results
The proposed technique is tested on the IEEE 30-bus, IEEE 57-bus, and
140 generator test systems and compared against the other evolutionary
methods. The results demonstrate that the proposed F-MSG algorithm
outperforms the other techniques. The minimum total cost rates and the
solution times obtained for each test system using the proposed
algorithm
are
significantly
lower
than
those
obtained
by
other
algorithms.
Keywords: Economic power dispatch; F-MSG algorithm; Non-convex fuel
cost rate curves; Prohibited zones; Security constraints; Valve point effect.
Under review