The increased penetration of renewables and the variable behavior of solar irradiation makes the energy storage important for overcoming several stability issues that arise in the power network. The current paper examines the design and stability analysis of a grid-connected residential photovoltaic (PV) system with battery–supercapacitor hybrid energy storage. The battery and supercapacitor packs are connected to the common 400 V DC-bus in. The increased penetration of renewables and the variable behavior of solar irradiation makes the energy storage important for overcoming several stability issues that arise in the power network. The current paper examines the design and stability analysis of a grid-connected residential photovoltaic (PV) system with battery–supercapacitor hybrid energy storage. The battery and supercapacitor packs are connected to the common 400 V DC-bus in a fully active parallel configuration through two bidirectional DC–DC converters, hence they have different voltage levels and their power flow is controlled separately. A detailed small-signal stability analysis is considered for the design of the current controllers for the bidirectional converters of the battery and supercapacitor. An important contribution here is that a detailed stability analysis is performed for both the boost and the buck mode of operation for the battery and supercapacitor converters, resulting in more accurate tuning of the controllers. Moreover, the small-signal stability analysis of the voltage source inverter (VSI) is considered in order to design the DC-bus voltage controller, where a reference output current is obtained using a phase-locked loop (PLL) for grid synchronization. The proposed model is developed and simulated in the MATLAB/Simulink software environment, based on mathematical analysis and average modeling. The simulation results verify the dynamic performance of the proposed model, through several rapid changes in PV generation and in load. ••Average model for grid-connected residential PV with battery–supercapacitor storage.••Detailed small-signal analysis of bidirectional DC–DC converter and DC–AC inverter.••Stability analyses for both boost & buck-mode of bidirectional DC–DC converter.••Results verify the dynamic performance under rapid changes in PV and load power.••PhotovoltaicsBatterySupercapacitorHybrid storageDC–DC bidirectional converterVoltage source inverterGridControl designCurrent rising electricity demand and climate change have reinforced the need for independence from conventional fuels and use of renewable energy sources. Solar photovoltaic (PV) is one of the most growing technologies in the world with a current growth rate of 35%–40% per year. Moreover, PV power generation can be considered as the most promising, widely available and essential renewable resource. On the other hand, the variable behavior of solar irradiation and, consequently, PV generation renders energy storage important for overcoming several problems that arise in the grid (Hemmati and Saboori, 2016, Argyrou et al., 2018a, Bocklisch, 2016).Additionally, the hybridization of energy storage technologies can allow various applications in a system that may not be possible for a single storage technology. A notable such example is the battery–supercapacitor storage, which combines the short-term (supercapacitor) and long-term (battery) storage, as well as the high power (supercapacitor) and high energy (battery) rating. Furthermore, supercapacitors can reduce stresses in battery storage and thus extend the battery life. The battery and supercapacitor pack are connected to the DC-bus through bidirectional DC–DC converters. The fully active parallel configuration provides flexibility as the battery and supercapacitor can operate in different voltages and be controlled separately (Argyrou et al., 2018c, Vazq. An essential part for the design of the control is the determination of the dynamic behavior of a converter. In other words, how the small variations of the inputs near the steady-state value affect the output of a converter. The goal here is to predict this low-frequency part, which allows us to design the controller of the converter (Erickson and Maksimovic, 2007).Classical control theory applies only to linear time-invariant (LTI) single-input single-output (SISO) systems, and it is not appropriate for the more demanding dynamic analysis of a nonlinear time-variant system. Therefore, for the latter case, it is necessary to develop a process that allows one to overcome the problems related to time-variation and nonlinearity of the switching process of the converter (Divya and Ajit, 2017). To this end, the necessary steps to be followed are graphically represented in Fig. 2. The resulting small-signal model is a LTI model in which all the standard circuit analysis techniques can be applied. To construct this, the nonlinear time-variant signal is averaged over one switching period, thus assuming that the switching ripples of the state variables are equal to zero as their time variance is removed. After that, the model is linearized by removing all the nonlinearities that incurred by the averaging process. Therefore, a linear time-invariant small signal model is produced, describing the time-domain dynamics at the presence of small-sign.
