## 1 Introduction  
Sizing of Distributed Generation (DG), Energy Storage Systems (ESSs), Smart house holds applications, and Demand Response (DR) strategies are all widely discussed issues, and analyzed in a large number of recent studies [1]. With reference to these areas, several studies address the problem of residential energy management. New challenges are emerging due to increasing photovoltaic (PV) generation, so that Energy Storage Systems (ESS) with distributed PV generators have been developed in different papers. However, a high diffusion of PV may cause critical issues (voltage rise) in a distribution system, thus different coordinated control systems are proposed [2, 3]. In order to minimize electricity customer cost, the management of power flow becomes a fundamental issue. In [4], an energy management system for a grid-connected PV-battery hybrid system is proposed, so that customers can benefit of demand response and a control method is developed to schedule the power flow. Numerous works evaluate these problems in terms of \"micro-grid systems\". In [5], some design considerations are presented for distributed micro-storage systems in residential applications. In this paper, the term \"micro-storage\" refers to small residential energy storage units with a capacity of few kilowatt-hours, and different micro-storage system architectures as well as analysis of system sizing are discussed. Other authors propose a DC micro-grid with a multilayer control and smart grid communications [6]. The control design permits a better DC micro-grid integration by avoiding undesired injection, mitigating fluctuations in the power grid and reducing grid peak consumption. Some studies focus on the characteristics of the converters in the micro-grid systems with the aim of improving the conversion efficiency. In [7], a hybrid system consisting of a PV array and rechargeable battery integrated to the distribution grid is presented. The system performs load sharing with the distribution grid by controlling the voltage source inverter (VSI), the boost and the buck-boost converters. The cost-benefits problem of solar PV technology is analyzed in [8; 9]. In [8], the authors propose a system with given PV modules and EES based on bank capacities to solve the daily energy flow control problem. Furthermore, in order to facilitate intensive penetration of PV production into the grid, a method is proposed in [9]. Peak shaving is realized with the minimal cost and power fluctuations on the grid are reduced by using a power supervisor based on a predictive power scheduling algorithm. A basic analysis study of stand-alone solar PV micro-grid power system is presented in [10]. The system is designed on the basis of residential load profile and solar exposure level in a particular area. In order to improve the integration of PV and energy storage systems, a power management strategy is designed to manage power flows between PV systems and an ultra-capacitor (UC) [11]. A numerical model that computes an optimized capacity of energy consumption is proposed in [12]. This model is based on weekly forecast with the aim of providing a stable energy that is insulated from the instability of weather change. The system is able to increase the energy consumption in normal days while maintaining minimum stable energy in bad weather conditions. To increase the use of PV energy in the residential applications, some researchers suggest a control of power flow and a selection of MPPT parameters for grid-connected PV systems with battery storage [13]. Other works discuss these issues in terms of innovative converter features for PV-battery systems [14]; a reconfigurable solar converter (RSC) is presented to perform dc/ac and dc/dc operations, by using a single-stage three phase grid-tie solar PV converter. A control method for the power electronic converters is discussed in [15]: the potential of utilizing battery energy storage for participating in primary frequency regulation of the grid is investigated.