Chris Train, director of market operations, said electricity margins - the difference between peak demand and available supply - were "tighter than we have seen historically" but that there was enough to meet the country's needs.
However regulator Ofgem says that risks to security of electricity supply - the dangers of the lights not being kept on - are now increasing at a faster rate than previously expected.
In its 2013/14 winter outlook report, National Grid said its central forecast was for an electricity margin of 5% during peak demand in cold weather, broadly in line with previous analysis. A spare 8% capacity was forecast for average temperatures.
Margins have been falling over the past few years, blamed on new laws on power station emissions and economic pressure to mothball old gas-fired power stations.
This has only partially been offset by a fall in peak demands amid energy saving measures and declining heavy industry, together with increasing wind generation and some new gas-fired power stations.
He said: "While there have been power station closures since last winter, the information suggests that the market can meet demand in cold weather.
"But as the system operator, we're never complacent and it's up to us to be ready to balance the system in real time. We believe we are ready and have the tools we need to play our part."
Concern about energy supply has been fuelled by reports that gas stores were driven "dangerously low" during the prolonged cold spell in March. However the new National Grid report said gas storage has increased since last year.
There is also ongoing public concern about high prices and profits made by the big energy firms amid a continuing squeeze on household incomes, resulting in a Labour pledge to freeze tariffs should the party win power.
But suppliers have warned that such price caps would have a damaging effect on the investment needed to maintain energy supply.