Unit Commitment Optimization Using Gradient-Genetic Algorithm and Fuzzy Logic Approaches - Complex System Modelling and Control Through Intelligent Soft Computations - page 675

algorithm methods is presented. Section 5 deals with the discussion of simulation
results and the main improvements of adopted strategies are highlighted. Finally,
Sect. 6 resumes the main conclusions followed by references.

2 Related Work

Since improvement of optimization techniques means decreasing costs of electric
power utilities and ensuring continuity of service and a better quality of energy,
great effort has been spent on finding a better optimization solution. The complexity

of the UC problem and the bene its of its solution improvement keep the research

continuously attractive. Therefore, a study of the literature on methods of solving
the Unit Commitment Problem (UCP) shows that various numerical optimization
techniques have been used to solve this problem. Indeed, dynamic programming
(Snyder et al. 1987 ; Guan et al. 1992 ; Ouyang and Shahidehpour 1991 ) is simple
but it requires enough computation time to converge to the optimal solution.
Dynamic programming searches the solution space for the optimal unit status. The
search can proceed in a forward or backward direction. The time periods of the
study horizon are known as the stages of the dynamic programming problem. Each
stage represents 1 h of operation. The combinations of units within the time period
are known as the states, and controls at the stage are again possible combinations of
units to be committed. The local cost function at a stage is the production cost in the
corresponding hour. Forward dynamic programming consists of two phases, a
forward recursion phase in which optimal paths to all reachable states at all stages
are established, and a backward recursion phase in which the optimal solution is
recovered starting from the feasible terminal state with the List cumulative cost.
As Merlin and Zhuang (Merlin and Sandrin 1983 ; Zhuang and Galiana 1988 ),
they adopted the method of Lagrangian relaxation because it was more effective
than the dynamic programming method due to its better quality of solution and
computation time rapidity. Therefore, Lagrangian Relaxation is the combination of
a dual optimization techniques and feasibility search procedures. The original
mathematical problem is known as the Primal Problem (PP). Corresponding to the
prima1 problem, the Lagrangian dual can be constructed. The Dual Problem (DP)
usually has lower dimensions than the PP and is easier to solve.
The Lagrangian dual of the unit commitment problem has a continuous and
convex objective function and is subject only to simple bounding constraints on the
solution variables. The Lagrangian Relaxation technique uses a different kind of
decomposition which generates lower dimension subproblems. Each subproblem
consists of determining the commitment schedule for a single unit over the planning
horizon. Each subsystem is solved independently, and the only link between these
subsystems is Lagrange multipliers, or so called pricing mechanism, which is
adjusted to ensure that the system constraints are met.
However, studies (Dekrajangpetch et al. 1999 ; Guan et al. 1992 ) have shown that
digital convergence and the quality of the solutions are not satisfactory whenever the