A novel and fast-converging cost minimization model using non-linear constrained mathematical programming (NLP) has been developed to optimize renewable and bioenergy generation and storage systems’ capacities for transitioning to an electricity system with net-zero greenhouse gas emissions. Running this temporal and spatial multi-scale model gives an in-depth understanding of realistic electricity mixes in sustainable transitioning. The model comprises three interactive modules 1) analytics and visualization of data inputs, climatic and demand time-series, and design configurations, and output results, optimal electricity mix, and storage characteristics, 2) mathematical models of renewable generation systems using non-linear climate-dependent capacity factor time-series and energy system components, and 3) NLP to minimize the total cost. Hourly and total energy balances are the crucial constraints influencing the speed and efficacy of the solution. Fast-converged solutions of the NLP model are updated considering battery energy storage with a few hours dispatch time for attainable optimum net-zero electricity (NZE) mix. The NLP optimization model is tested on the energy-intensive UK South. The feasible optimum regional solutions characterized as high renewable supply-medium-to-high-demand (South West), low-supply-medium-demand (Greater London), and high-supply-high-demand (South East) scenarios are projected to the UK national level. The inputs to the NLP model are wind speed and solar radiation with annual hourly resolutions curated from the Centre for Environmental Data Analysis, process economic parameters (investment, fixed, operating, and resource costs, weighted average cost of capital, and life in years of processes) from the LUT energy system model, and global warming potential impacts from our archived literature. 2020-2050 electricity mixes are analyzed with varying costs and demands. The NLP optimization followed by energy storage feasibility analysis gives the following attainable optimal energy mixes: wind: 55%, solar: 29%, hydro: 0.5%, geothermal: 0.4%, and bioenergy: 1% (high-supply-medium-to-high-demand); wind: 52%, solar: 32%, hydro: 0.5%, geothermal: 0.5%, and bioenergy: 1% (low-supply-medium-demand); and wind: 45%, solar: 23%, hydro: 0.7%, geothermal: 0.7%, and bioenergy: 10% (high-supply-high-demand). Energy storage (13.5 TWh in the UK South) with 13-22% contributions of load demand (80 TWh in the UK South) costs 14% of the levelized cost of electricity production, 120-190 EURO/MWh. The high-supply-medium-to-high-demand scenario, providing the UK NZE projection of wind: 40GW, solar: 21GW, bioenergy and other renewables: 5GW, nuclear: 6GW, and gas with carbon capture, utilization, storage, and sequestration (CCUS): 5GW by 2050, mirrors the government's NZE plan. The additional wind (currently at 8.65GW), solar (currently at 1.5GW), and CCUS (currently there is none) capacities require £23 billion, £4 billion, and £1 billion investment costs.