## 1 Introduction
In [20], the authors presented a protection coordination strategy considering photovoltaic units with different levels of penetration and locations along the DN; in general terms, they modified the characteristic curves of OCRs by varying the time multiplying setting (TMS) while keeping the pick up current fixed. Microgrids and modern DNs feature different operational modes, which makes it more complex to achieve optimal settings of OCRs. For overcoming this issue, a constraint that involves the plug setting multiplier (PSM) was presented in [10]. The PSM is defined as the ratio between the fault current measured by the relay and the pickup current. The overcurrent relay tripping characteristic is restricted by the value of the PSM. Standard commercial relay characteristic curves are usually designed in a range in which the minimum value is 1.1 times the PSM, whereas the maximum value is 20 times this value. DG units in DNs significantly magnify the short-circuit level. Hence, for several faults, this defined maximum PSM value could be surpassed, impacting the protection sensitivity and leading to the loss of the coordination protection scheme. The new constraint presented in [10] addresses the above conditions by setting the maximum value of 20 times the PSM. In this case, the optimal coordination problem was solved using a genetic algorithm (GA). The authors in [11] implemented the constraint proposed in [10]; however, they used a non-standard curve to improve the efficiency of the OCR protection. This non-standard curve alters the region of the characteristic curve by considering a value of 100 times the PSM for its maximum value. In [21], the authors considered the upper limit of the PSM as a variable instead of a fixed parameter, as usually done in traditional approaches, and solved the coordination problem by means of a GA.  
Smart and adaptive protection schemes are required for modern DNs. In this scenario, user-defined and non-standard features of OCRs should be implemented to meet the new challenges imposed by modern DNs and microgrids; however, they require specialized solution methods. For this reason, this paper proposes a hybrid harmony search and simulated annealing (HS-SA) algorithm for the solution of the coordination problem in modern DNs that integrate DG. Harmony search (HS) is a comparatively easy but efficient evolutionary algorithm. In the HS algorithm, a collection of plausible solutions is generated randomly. A new candidate solution is produced using all available solutions in the harmony memory (instead of only two as in the GA). If this new generated solution is better than the worst current solution in the harmony memory, the worst solution is substituted by this one. In this paper, the hybrid HS-SA algorithm proposed in [22] was implemented. SA introduces diversification in the search process and allows the HS to escape from locally optimal solutions. The efficiency and benefits of HS have been proven in several applications of electrical engineering, including optimal network reconfiguration [23] and harmonic elimination [24]. Additionally, hybrid versions of HS have been proposed in the domains of data mining [25], electricity price forecasting [26], job-shop scheduling [27] and constrained optimization [28], among others. As regards the protection coordination problem, HS was implemented in [29; 30; 31] to approach the optimal coordination of directional OCRs. The authors in [29; 30] present applications for traditional power systems and interconnected power systems, respectively, while in [30], DG is also considered in the coordination problem. However, none of these previous works consider the protection coordination from the point of view of modern DNs. Instead, they solve the problem in power systems which operate at higher voltage levels; also, they do not consider different operative scenarios.