This paper presents proof-of-concept of a novel photovoltaic (PV) inverter with integrated short-term storage, based on the modular cascaded double H-bridge (CHB²) topology, and a new look-up table control approach. This topology combines and extends the advantages of various distributed converter concepts, such as string inverters, microinverters, and cascaded H-bridge (CHB) multilevel inverters. The proposed CHB² inverter incorporates individual PV elements into modules that can dynamically connect to their neighbors not only in series but also in parallel, which reduces conduction losses and enables simple module balancing. Maximum-power-point tracking of the PV element is performed in each module. As a demonstration of the flexibility of the approach and to filter large power fluctuations before they enter the grid, each module further incorporates batteries for energy storage, which enables continuous power output by compensating solar power fluctuations, while the CHB² can balance the batteries’ load and state of charge. The inverter provides exceptionally high output quality without large filters, since the multilevel ac output is finely quantized. The elimination of extensive output filtering provides for an extremely rapid dynamic response as well. We furthermore introduce an optimized, computationally efficient, look-up-table-based controller and module scheduler which leverages the large number of degrees of freedom provided by the flexible series-parallel CHB² configurations to optimize conduction loss, switching loss, and load balance. The method can be extended to CHB² circuits in general to improve their performance while simplifying control. Finally, we demonstrate that the inverter is robust to open-circuit failure of power switches or PVs.