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In the present paper we consider a class of multiobjective B-vex programming problems involving differentiable B-vex n-set functions and establish duality results in terms of properly efficient solutions. Further, we relate the problem to a certain saddle point of a Lagrangian and show multiobjective fractional program as a special case of the main problem. ᮊ

Abstract. This paper proposes a load frequency control scheme for an autonomous hybrid generation system consisting of wind turbine generator (WTG), diesel engine generator (DEG), fuel cell (FC), aqua electrolyzer (AE) and battery energy storage system (BESS). In wind power generation systems, operating conditions are changing continually due to wind speed and load changes, having an effect on system frequency. Therefore, a robust controller is required for load frequency control. The control scheme is based on Linear Matrix Inequality (LMI)-Linear Quadratic Regulator (LQR). The control optimization problem is obtained in terms of a system of LMI constraints and matrix equations that are simultaneously solved. The proposed load frequency control scheme with the advanced LMI-based-LQR (ALQR) design is applied for the autonomous hybrid generation system. The effectiveness and robustness of the proposed controller is demonstrated for different load and wind power perturbations. The results suggest superior performance of the proposed ALQR controller against an optimal output state feedback controller. The integrated control could be realized though the web by applying Internet of Things technologies within the future smart grid.