## 1 Introduction  
Energy supply deficiency and climate change have resulted in the rapid growth of distributed generation technology [1]. This growth can also be attributed to the cleaner renewable sources that constitute most DGs and aging equipment [2, 3]. Distributed generation has numerous definitions and names like dispersed generation, embedded generation and decentralized generation. But, among all these terms, distributed generation is the most common [4, 5]. Distributed generation, irrespective of its advantages, can cause instability in voltage and other power practices like the power factor, reactive power and frequency when interconnected to an existing grid [6, 7, 8]. The instability problem can occur as a result of the intermittency of renewable sources, non-radial power flow, over-voltageand management [9]. Most of the practical distribution power networks have been designed to operate on a one-directional power flow feeder, most commonly known as a radial system [10; 11; 12]. With these radial systems, protection schemes have become rather standard and also straightforward, and this is based on common phase and neutral/ground non-directional overcurrent protection [2]. However, the addition of DG to existing radial systems would change this basic protective system in terms of design and structure to accommodate the integration of DGs in these systems. Consequently, challenges including keeping required voltage levels within preferred limits are bound to manifest [7; 13]. That is why a careful and analytical investigation needs to be performed on all power and protective systems before DG integration to avoid the complete breakdown of these entire systems [13]. It is for this reason that a maximum allowable penetration is recommended at every interconnection point of DG [14]. Apart from the voltage stability problem, there exists an angle stability problem and a frequency stability problem, but both the angle problem and the frequency problem are not often seen in distribution systems [15]. A grid-tied or micro-grid system can be referred to as autonomous, and its mode of interconnection may be based on an inverter system for solar PV and energy storage devices or a synchronous or induction motor system for wind generation and standard fossil fuel-based motor generators [4]. There are other factors that affect voltages in distribution systems besides the connecting generator in the distribution system. Ordinarily, without DG, the distance of the transmission or the length of the cable brings about variation in voltage profiles [12]. When a DG is connected, the location of the DG, DG output or capacity, DG dispersion, the feeder's conductor, the load profile and the primary voltage setting are the factors that can equally vary the voltage profile of the distribution system [16; 17]. Increasing DG output could either be increasing the real power or the reactive power but in most cases the active power [18; 19] midst the other factors, location of DG which is the distance from the substation to the customer point is an important consideration in the study of voltage stability due to voltage drop [20]. Voltage will rise due to DG integration and this rise is directly proportional to the distance (linear) with the distance along the line to the point of DG connection [21]. In recent times, under-voltage has been one of the major areas in the active stream of research on radial distribution systems that are dominated by distributed generators. The increasing load on existing power system infrastructure has continued to stretch the nominal voltage [4]. The growth in the population and the advent of technology have also contributed to the sharp load increase, which may be inadequate to meet future demands [22]. Considering the above, electric utilities and researchers have carried out several investigations on DG to know how DG will affect existing system structures when used as an alternative resource to aid overwhelmed power system structures and operations [23; 24; 25; 26].