Modern energy systems face an unprecedented shift toward renewables, electric mobility, and the electrification of industries and households. This trend places new demands on grid stability and calls for agile, cost-effective solutions. DC microgrids are increasingly explored as a viable technology because they mesh naturally with battery energy storage, photovoltaic (PV) generation, and other renewable sources, all of which inherently produce or consume dc power. Conventional coordination schemes often rely on supervisory communication networks and centralized controllers, which add cost, enlarge the cyberattack surface, and complicate maintenance.

The article traces the evolution of numerical tools from the Renaissance to the present. It examines the flourishing of numerical methods and concepts in the nineteenth century, particularly in relation to the development of new scientific fields, ranging from thermodynamics to electromagnetism and beyond. The increasingly demanding scientific challenges posed by industrialization necessitated more sophisticated mathematical techniques in the early decades of the twentieth century, leading to the introduction of mechanical and electromechanical computers—both analog and digital—in the 1930s. The enhanced computational capabilities of these machines, in turn, facilitated the development of more advanced mathematical methods. A major revolution occurred with the advent of digital electronic computers in the 1950s, owing to their vastly superior computational speed. Specialized methods were soon developed on electronic computers from the 1960s onward, including early software precursors to MATLAB and Maple. The article then traces the development of advanced mathematical methods and software for electric grid analysis, such as SPICE and FastSPICE. The principal methods for continuum media analysis are also described, including finite differences, finite elements (e.g., NASTRAN, ASKA, and SAP), and other techniques such as finite volumes, boundary elements, and meshfree methods. Sections are devoted to Computational Electromagnetics and Coupled Programs, which are handled by software such as ANSYS, ABAQUS, FEAP, and COMSOL. Finally, the evolution of numerical optimization methods—both deterministic and stochastic—is outlined.

Creating a sustainable future is a transdisciplinary challenge where industrial electronics (IE) plays a key role by providing environmentally friendly solutions to daily processes. Domestic device electrification is a powerful tool for sustainable energy consumption and indoor air quality improvement. In this context, this article covers a relevant example of household appliance electrification with improved energetic performance: domestic induction heating. Domestic IH has now been on the market for 50 years. This article reviews the main historical milestones in electrical cooking appliances, and presents the enabling technologies and advances behind the success of current IH technology. Additionally, recent technological development advancements and future trends are introduced showing the potential of IH to help pave the path to create a sustainable future.

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