<span>This paper presents a</span><span lang="EN-US"> voltage </span><span>sensitivity analysis </span><span lang="EN-US">with respect to the real power injected </span><span>with</span><span lang="EN-US"> renewable energies</span><span> to determine the optimal integration of distributed generation (DG) in distribution systems (DS).</span><span> <span lang="EN-US">The best nodes where the power injections improve voltages magnitudes complying with the constraints are determined.</span></span><span> As it is a combinatorial problem, p</span><span lang="EN-US">article swarm optimization (PSO) and simulated annealing (SA) were used to change injections from 10% to 60% of the total power load using solar and wind generators and find the candidate nodes for installing </span><span>power </span><span lang="EN-US">sources. The method was tested using the 33-node, 69-node and 118-node radial distribution networks. The results showed that the best nodes for injecting real power with renewable energies were selected for the distribution network</span><span> by using the voltage sensitivity analysis</span><span lang="EN-US">. Algorithms found the best nodes for the three radial distribution </span><span>networks</span><span lang="EN-US"> with similar</span><span> values in the maximum injection of real</span><span lang="EN-US"> power</span><span>, suggesting that this value maintains for all the power system cases</span><span lang="EN-US">. The injections applied to the different nodes showed that voltage magnitudes increase significantly, especially when exceeding the maximum penetration of DG. The test showed that some nodes support injections up to the limits, but the voltages increase considerably on all nodes.</span>

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Grid side converters of renewable power plants have to be capable of dealing with severe grid disturbances, such as, grid faults and voltage sags. Model‐based predictive control provides outstanding performance to grid side converters: fast dynamic response, good tracking error and high‐quality currents. However, choosing the best set of vectors for the modulation requires assessing all the possible combinations of vectors using a cost function, which is very time consuming. Thus, the modulation is normally carried out with only 1 or 2 vectors per PWM period to save computing time, but this turns the modulation non‐linear. This lack of linearity makes it impossible to use symmetrical components in unbalanced grids. A linear multi‐vector model‐based predictive control that controls the power of both sequences using a sole cost function and analyses the effect of the transient response of several sequence decomposition systems on the model‐based predictive control predictions and dynamic response is proposed. Moreover, the proposed multi‐vector provides low THD currents while keeping the computing time low. In addition, the paper addresses the extrapolation of the proposed multi‐vector model‐based predictive control to N‐level converters. The good performance obtained is supported by the results obtained in simulations and the laboratory.