## 1 Introduction
In [27] different load models have been introduced and studied in order to achieve minimum active and reactive power losses in the network. In [28] an analytical method has been introduced to minimize the power losses and improve the system profiles based on the available specific scenarios. In [29] optimum location of a single DG with unity power factor has been studied. In [30] the authors proposed an analytical approach for losses minimization for DGs allocation, but this method is depended on installing DG units sequentially one-by-one. In [31; 32], the authors proposed an analytical approach for losses minimization indicating the optimal sizing and siting for single DG unit with non-generated reactive power. However, in [33], the authors produced a new method which can be used to determine the optimal sittings for multiple DG units which are non-generative of the reactive power without determining the optimal capacities of these DG units. In [34], the authors produced an approach which can be used to determine the optimal capacities and sittings for multiple DG units which also consume the reactive power. In [35], the authors produced an algorithm to determine the optimal sizing and sitting for any type of the DG unit, but it cannot be used for multiple DG units. Also, in [7] the authors produced an analytical approach to determine the optimal capacity and location for a single DG unit for known power factor. In [36], the authors suggested a new hybridized method which is a combination of analytical approach and heuristic search which was proposed to find the optimal locations of multiple DGs of multiple types. The authors of [37] have proposed an approach to allocate a DG unit with unity power factor. Later on, this approach has been extended in order to involve allocating a single DG that is capable to generate real and reactive power, this approach is named as an improved analytical (IA) method [38]. After that, the IA method has been upgraded to involve the case of multiple DG interconnection [39]. It is worthy to mention that the solutions obtained by those methods have been compared with the proposed approach in this paper. The above review clearly shows that considerable researches have been done for optimally planning of DGs; however, in some methods it is assumed that DG power factors are not state variables but specified values. Moreover, some methods are not able to provide the optimal solution for the allocation of a number of DGs. Furthermore, some algorithms represent the DG optimization problem correctly but these algorithms did not succeed to deal with number, location, capacity, and power factor of the DG units simultaneously. On the other hand, many researches proposed methods that successfully represent DG optimization problem, but these methods need intensive computational capabilities. The main contribution of this paper is to develop a new analytical method for optimally planning of DGs in order to minimize the power loss in distribution networks. The proposed method developed analytical expressions that has been initiated, formulated, and solved in a simplified manner by finding the optimal capacities, locations, and power factors of the DG units added to the system by referring to the resistances of the distribution lines in which the current pass through and hence efficiently provides an accurate optimal solution without using intensive computational capabilities. On the other hand, the proposed method is based on simple algorithm via basic mathematical models. Therefore, it can be easily extended to consider the load variation and intermittent nature of RES-based DGs. This paper is organized in five sections and the rest of the paper is prepared as follows: Section 2 gives a brief introduction about DG technology; this section includes a grid interconnection pros and cons. In addition, major DG types and capacity are addressed in this section. Section 3 introduces the mathematical representation and present detailed descriptions of the proposed approach.