An improved binary particle swarm optimization for unit commitment problem PDF

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This paper proposes a new improved binary PSO (IBPSO) method to solve the unit commitment (UC) problem, which is integrated binary particle swarm optimization (BPSO) with lambda-iteration method. The IBPSO is improved by priority list based on the unit characteristics and heuristic search strategies to repair the spinning reserve and minimum up/down time constraints. To verify the advantages of the IBPSO method, the IBPSO is tested and compared to the other methods on the systems with the number of units in the range of 10–100. Numerical results demonstrate that the IBPSO is superior to other methods reported in the literature in terms of lower production cost and shorter computational time.


  • Unit commitment;
  • Priority list;
  • Particle swarm optimization;
  • Heuristic search

1. Introduction
Unit commitment (UC) is a very significant optimization task,
which plays an important role in the operation planning of power
systems. The unit commitment problem (UCP) in power systems
refers to the optimization problem for determining the start-up
and shut-down schedule of generating units over a scheduling per-
iod so that the total production cost is minimized while satisfying
various of constraints. UCP can be considered as two linked optimi-
zation decision processes, namely the unit-scheduled problem that
determines on/off status of generating units in each time period of
planning horizon, and the economic load dispatch problem. Math-
ematically, the UCP has commonly been formulated as a complex
nonlinear, mixed-integer combinational optimization problem
with 0–1 variables that represents on/off status and continuous
variables that represents unit power, and a series of prevailing
equality and inequality constraints. However, the number of com-
binations of 0–1 variables grows exponentially as being a large-
scale problem. Therefore, UCP is known as one of the problems
which is the most difficult to be solved in power systems.
Many methods have been developed to solve the UCP in the
past decades. The major methods include priority list method
(PLM) (Senjyu, Miyagi, & Saber, 2006), dynamic programming
(DP) (Su & Hsu, 1991), branch-and-bound methods (BBM) (Cohen
& Yoshimura, 1983), integer and mixed-integer linear program-
ming (MILP) (Khodaverdian, Brameller, & Dunnitt, 1986; Samer &
John, 2000), Langrangian relaxation (LR) (Feng & Liao, 2006; Ongsa-
kul & Petcharaksm, 2004). Among these methods, PLM is simple
and fast, but the quality of final solution is not guaranteed. DP is

flexible but the disadvantage is the ‘‘curse of dimensionality”,
which results it may leads to more mathematical complexity and
increase in computation time if the constraints are taken into con-
sideration. The shortcoming of BBM is the exponential growth in
the execution time with the size of UCP. MILP adopts linear pro-
gramming techniques to solve and check for an integer solution.
MILP for solving UCP fail when the number of units increases be-
cause they require a large memory and suffer from great computa-
tional delay. These methods have only been applied to small UCP
and have required major assumptions that limit the solution space.
The main problem with the LR is the difficulty encountered in
obtaining feasible solutions. Due to the non-convexity of the
UCP, optimality of the dual problem does not guarantee feasibility
of the primal UCP. Furthermore, solution quality of LR depends on
the method to update Lagrange multipliers.
Aside from the above methods, meta-heuristic approaches such
as artificial neural networks (ANN) (Dieu & Ongsakul, 2006),
genetic algorithm (GA) (Damousis, Bakirtzis, & Dokopoulos, 2004;
Kazarlis & Bakirtzis, 1996; Senjyu, Yamashiro, & Uezato, 2002),
evolutionary programming (EP) (Juste, Kita, & Tanaka, 1999),
memetic algorithm (MA) (Jorge & Smith, 2002), Tabu search (TS)
(Mantawy, Abdel, & Selim, 1998), simulated annealing (SA) (Zhu-
ang & Galiana, 1990), particle swarm optimization (PSO) (Lee &
Chen, 2007; Ting, Rao, & Loo, 2003) and greedy random adaptive
search procedure (GRASP) (Viana, Sausa, & Matos, 2003) have also
been used to solve UCP since the beginning of the last decade.
These meta-heuristic methods optimization methods attract much
attention, because of their ability to search not only local optimal
solution but also global optimal solution and can easily deal with
various difficult nonlinear constraints. However, these meta-heu-
ristic methods require a considerable amount of computational
time to find the near-global minimum especially for a large-scale


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