**4. Optimization Models and Methods for BESS/PVDGs Allocation**

The design and planning of battery energy storage system–photovoltaic distributed generation system is a research area that has continued to generate a lot of interest from many researchers, hence the large number of literature studies on the topic. The planning problem mentioned above concerns the hybrid energy systems that have optimal patterns and whose optimal sizes, placement/location and type of generation components/units can be assigned with minimum costs over the lifetime of the technologies. Therefore, the planning by the minimum net present value (NPV) of cost is called the optimal planning or optimal allocation of all probable hybrid technologies that are in optimal transition [11,24,56,58].

There are several methods for obtaining an optimal planning solution and many realtime, commercially available software applications for energy systems integration. In addition, various researchers have applied different optimal techniques to solve BESS/PVDG allocation problems. Different optimization methods, such as conventional methods, population-based intelligence search methods, some promising heuristic intelligence search approaches and commercial software applications, have been applied by the researchers to optimize hybrid BESS/PV distributed generation systems.

#### *4.1. Conventional Optimization Methods*

Conventional optimization methods are analytical and numerical techniques that usually present numerical equations to resolve optimal allocation problems. The methods involve computations, mathematical and theoretical analysis. The accuracy of these methods greatly depends on the efficacy of the model formulated. The advantages of these methods are the ease of implementation and short computation time to obtain convergence for the problem. However, under a complex problem, the accuracy of the solution may not be satisfactory because of the hypotheses used in simplifying the problem. Some of the conventional methods are discussed as [2,57–59].

#### 4.1.1. Sensitivity Analysis Methods

Sensitivity-analysis-based methods use sensitivity indices used to optimally allocate DG units. In these methods, the original nonlinear equations are linearized about their starting operating points to lower the numbers of feasible solutions in the search space. The advantages of sensitivity analysis methods are reduced computation time, which is critical for large practical systems, and good ability to assess the uncertainties of renewable energy resources. Anuradha et al. [60] present a loss-voltage sensitivity index for optimizing the renewable DG size, BESS capacities and power dispatch in distribution networks. The objective is to simultaneously evaluate both minimum effects of network losses and voltage variations for optimizing the DG size [60]. A hybrid of loss sensitivity analysis methods and novel voltage stability index is applied by Murty and Kumar [61] to find optimal sizes and locations of active and reactive power DGs. The objective is to minimise copper losses and enhance network voltage profile. In Saini and Gidwani [62], a comprehensive assessment of battery energy storage system installation and the placement of photovoltaic (PV) units in a radial distribution network is performed utilizing different load models. The objective is to minimise annual energy losses, control overvoltage and reverse power flow problems in a distribution network. Nevertheless, the solutions obtained from the sensitivity analysis methods solely found optimal placements of distributed generators, but the levels of optimality of such solutions are not known [4,58].
