Abstract
The controlling parameter tuning of the hydraulic turbine governing system (HTGS) is always deduced under single operating condition and is not suitable for the changeable operating conditions of the hydraulic turbine. For this purpose, multiobjective optimization problem of fractional order PID (FOPID) controller for HTGS is constructed through the consideration of no-load disturbance and on-load disturbance operation conditions, where the performance indicators of integral time absolute error (ITAE) under both operation conditions are employed as the objective functions. To achieve the optimum, the multiobjective version of newly proposed Harris hawks optimization (MOHHO) is established to solve the optimization issue. Additionally, hybrid strategies which include Latin hypercube sampling initialization, modified differential evolution operator, and mutation operator are coupled into MOHHO (HMOHHO) to promote the global searching capability. Simultaneously, the linear model of rabbit energy within MOHHO is replaced with a nonlinear one to further enhance the searching capacity. Subsequently, the effectiveness and superiority of the proposed HMOHHO are verified by several multiobjective UF and ZDT test problems. Finally, the practical application and contrastive analysis ascertain that the constructed multiobjective problem of FOPID controller is suitable for HTGS under changeable operating conditions, and the proposed HMOHHO is effective in solving the issue.
Highlights
Introduction e EnergyInternet [1] is called the core technology of “the third industrial revolution,” which aims to replace fossil energy with renewable energy [2] and has attracted sufficient attention worldwide. e Energy Internet heightens the proportion of renewable energy gradually in primary energy production and consumption, to establish a sustainable energy supply system
The practical application and contrastive analysis ascertain that the constructed multiobjective problem of fractional order PID (FOPID) controller is suitable for hydraulic turbine governing system (HTGS) under changeable operating conditions, and the proposed HMOHHO is effective in solving the issue
In HMOHHO, the rabbit position in archive set is selected by leader selection mechanism, during which process the computational complexity can be denoted by O(A). en, computational complexity of location updating can be denoted by O(N ∗ dim)
Summary
2.1. eory of Fractional Calculus. e research of fractional calculus [44] has been carried out since 1960s and widely expanded into the fields of science and technology. There are always some complex issues which make it difficult to explain the model with integer order calculus, while fractional calculus shows more flexibility and availability. For this purpose, the theory of fractional calculus is introduced and employed to promote the controller modeling for HTGS later. E parameters λ and μ of FOPID controller can be set any real number between 0 and 2, which is a generalized form of traditional integer order PID controller. Compared with the traditional integer order PID controller, the parameter tuning of FOPID controller increases the complexity of algorithmic calculation process to a certain extent due to the additional two parameters. Λ, μ > 0, where λ 1 and μ 1; it is the traditional PID controller model
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