 Solution

Take a fully backed-up peak demand of $60$ GW, an illustrative gas capacity capital cost of £$500$/kW, and an annual capital-recovery factor of $0.10$. The installed cost is £$30$ billion, so the annual capital charge is £$3$ billion. Spread over an illustrative annual electricity consumption of $300$ TWh,A doubled capital-cost assumption doubles this charge. This estimate counts backup capacity even if it runs rarely, which is why capital rather than fuel can dominate its fixed annual cost.

It is not the total cost of a renewable or gas system. Fuel, emissions, maintenance, staffing, gas supply during correlated cold weather, network capacity, startup constraints and reliability standards remain additional considerations. Backup requirements need not equal the sum of intermittent nameplate ratings; demand correlation, capacity credit, interconnection and storage matter. The arithmetic shows that a large reserve power rating can have a modest annualized capital charge per unit of total electricity, while leaving substantial practical and environmental constraints unresolved.