In this paper, we present an improved version of the infeasible-interiorpoint method for linear optimization introduced by Roos (SIAM J Optim 16 (4): 2006). Each main step of Roos's algorithm is composed of one feasibility step and several centering steps. By using a new search direction, we prove that it is enough to take only one step in order to obtain a polynomial-time method. The iteration bound coincides with the currently best iteration bound for linear optimization problems.

The continuous stability of hybrid microgrids (MGs) has been recently proposed as a critical topic, due to the ever-increasing growth of renewable energy sources (RESs) in low-inertia power systems. However, the stochastic and intermittent nature of RESs poses serious challenges for the stability and frequency regulation of MGs. In this regard, frequency control ancillary services (FCAS) can be introduced to alleviate the transient effects during substantial variations in the operating point and the separation from main power grids. In this paper, an efficient scheme is introduced to create a coordination among distributed energy resources (DERs), including combined heat and power, diesel engine generator, wind turbine generators, and photovoltaic panels. In this scheme, the frequency regulation signal is assigned to DERs based on several distribution coefficients, which are calculated through conducting a multi-objective optimization problem in the MATLAB environment. A meta-heuristic approach, known as the artificial bee colony algorithm, is deployed to determine optimal solutions. To prove the efficiency of the proposed scheme, the design is implemented on a hybrid MG. Various operational conditions which render the system prone to experience frequency fluctuation, including switching operation, load disturbance, and reduction in the total inertia of hybrid microgrids, are studied in PSCAD software. Simulation results demonstrate that this optimal control scheme can yield a more satisfactory performance in the presence of grid-following and grid-forming resources during different operational conditions.