This chapter discusses the development and application of an intelligent computational technique called binary whale optimization algorithm (BWOA) and its application to solve the unit commitment (UC) problem. The whale optimization is a heuristic approach that mimics the intelligence associated with hunting and feeding behaviour of whales. The two distinct properties of location updates of whales, namely shrinking approach and spiral update approach are used for optimizing the position of prey. To improvise the real-valued whale optimization algorithm for binary UC problem, update process of whale position is mapped to binary search space using various transfer functions. The binary variants include three sigmoidal transformations and two tangent hyperbolic transformations. The binary variants presented are evaluated using extensive numerical experiments on various test systems and operating conditions. The simulation results are presented and compared to various existing classical/traditional, heuristic and meta-heuristic approaches. In addition, the statistical significance of proposed BWOA approaches among other binary approaches and within themselves is verified using a series of standard statistical tests. The same demonstrates the effectiveness of proposed BWOA to solve UC problem of small, medium and large scale.

Chapter Contents:

• Abstract
• 11.1 Introduction
• 11.2 Problem formulation
• 11.2.1 Nomenclature
• 11.2.2 Objective
• 11.2.3 Constraints
• 11.3 Binary whale optimization algorithm
• 11.3.1 Overview of WOA
• 11.3.2 Continuous valued WOA
• 11.3.2.1 Binary whale optimization algorithm
• 11.4 BWOA implementation to UC problem
• 11.4.1 Representation of binary variables of UC problem
• 11.4.2 Binary whale position initialization
• 11.4.3 Binary whale position update
• 11.4.4 Binary valued solution for UC schedule
• 11.4.5 Unit output continuous valued variables
• 11.4.6 Termination criteria
• 11.4.7 Constraint handling
• 11.4.7.1 Minimum up/down constraints
• 11.4.7.2 Spinning reserve and load satisfaction repair
• 11.4.7.3 Decommitment algorithm under excessive spinning reserve
• 11.5 Numerical results and discussion
• 11.5.1 Performance of BWOA for test system 1
• 11.5.2 Performance of BWOA for test system 2
• 11.5.3 Comparison of proposed approaches with various other approaches
• 11.6 Statistical analysis
• 11.6.1 Friedman test
• 11.6.2 Friedman aligned ranks test
• 11.6.3 Wilcoxon pairwise comparison
• 11.6.3.1 Quade test
• 11.7 Conclusion
• References

Inspec keywords: statistical testing; search problems; power generation scheduling; power generation dispatch; optimisation

Other keywords: intelligent computational technique; whale hunting behaviour; tangent hyperbolic transformations; whale position update process; sigmoidal transformations; shrinking approach; meta-heuristic approaches; binary search space; BWOA approaches; binary whale optimization algorithm; standard statistical tests; prey position optimization; real-valued whale optimization algorithm; spiral update approach; heuristic approach; power system operation; binary UC problem; unit commitment problem; binary variants; whale feeding behaviour

Subjects: Power system management, operation and economics; Optimisation techniques; Combinatorial mathematics; Other topics in statistics