## 1 Introduction  
Distribution systems are the key structures, which create a connection between transmission system and the consumers, in power systems. Although conventional distribution systems used to satisfy most of the needs, distribution system operators (DSOs) are encountering many new problems due to the emergence of new technologies, such as integration of renewable energy resources, storage devices and electrical vehicles. Some of the common issues are efficiency problems in energy conversion, rapid changes in demand and bi-directional power flows [1]. Recently, with the integration efforts of the renewable energy sources, traditional passive distribution networks which were created based on \"install and forget\" philosophy are becoming active distribution networks. The existence of distributed energy resources (DERs) in the distribution networks may affect the system operation. With the inverters connected close, the power outputs may be adjusted to overcome problem such as reverse flows, over-under voltage problems. Moreover, microgrids that can operate either connected to distribution networks or in islanded operating modes are becoming popular recently. The history of microgrids goes back to the end of the 19 th century; the case of Pearl Street Station [2] was one of the initial microgrid applications worldwide. They have again become popular in the 21 st century. During the Sandy super-storm, the importance and effectiveness of the microgrids were understood again because of the help of microgrids to distribution networks on keeping power on. According to [1], microgrids can be defined as interconnected distribution systems which can work in either grid connected or islanded modes. A more detailed definition is as follows. Microgrids are isolated power systems that can be connected to the main grid and consist of several components such as photovoltaics (PVs), wind turbines (WTs), generators, battery energy storage systems, etc. Distribution system operators try to keep the voltage magnitudes in the allowed ranges which are generally \(\pm 5\%\) as given in the IEEE Guide [3]. More specifically, if the voltage deviations through the system are low, this also causes the power losses to be low as well. As it is known, in a radial (a distribution or a microgrid) system the voltage level monotonically decreases towards the consumers. However, with the introduction of DERs this fact has changed, and DERs yield bi-directional power flows on distribution systems. Thus, the impacts of DERs on distribution networks is a challenging issue. To keep voltage magnitudes in desired ranges, conventional approach is to use tap changer transformers and switched bank capacitors [4], however recently with the technological developments related to power electronics, inverters are started to be used together with those in a coordinated way [5; 6]. In [7], PV hosting capacity of feeders using reactive power controls and tap changer operations was examined. Although DERs have various advantages, e.g., make the islanded mode of operation possible, they may also jeopardize the system operation in terms of applicable voltage limits [8; 9; 10; 11]. Generally renewable sources are connected to the main grid with an inverter, most of the industrial inverters are using maximum power point tracker (MPPT) algorithm to maximize the power production. Hence, the output characteristics of the DERs should be controlled to prevent voltage level related problems. Various works can be found in literature to solve this specific problem. In [8], it is shown that inappropriate use of On/Off control procedure may result in sequential loss of the DERs. Therefore, global and local active power curtailment methods are proposed, where the former approach seeks for communication and coordination--the latter one does not guarantee the optimal solution [8]. Authors in [9] try to keep the voltage level in permissible limits by controlling the reactive power output of the DERs by considering the supplied active power.