We have entire Zed-Carbon design units and Solar Decathlon projects, and many researchers and professors in our Department of the Built Environment trying to work this one out! The answer is never clear - which is why we keep repeating the exercise every year. And we must avoid answering that it can be done by offsetting (lazy thinking, "leave it all to someone else"). If off-setting works, then we are already Carbon Zero, and we can stop trying.
Perhaps Only the combination of many different ideas.....
• Biomass - Heating with Wood burning stove (to avoid using gas, and wood is notionally carbon zero), and
• 4kW or more south facing PV for the electric (for cooking and lighting and heat reclaim),
• Solar conservatory (get reclaimed heat from),
• Whole house Heat reclaim (from conservatory, cooking, incidental gains etc)
• Heavy thermal mass (storage) and
• High insulation (keep it stored),
• Wind turbine for generation when the sun doesn't shine, and
• The rest of the roof in grass (to replace oxygen)
• Batteries to store excess power, or a connection to the Public Grid (which is a societal cost)
• Bicycle storage, woodshed, potting shed...
......will yield a carbon zero house... through design, not offsetting.
Yes .... if you haven't noticed, we have virtually described the Hockerton houses, except for the wood burning. It takes that level of commitment to get it right.
Plus of course the 'Societal costs':
• Rainwater capture and sterilization to avoid societal costs of delivering water.
• Biodigester to avoid societal costs of sewage disposal.
• Plus enough Land to grow food and a few pigs/sheep/chickens to avoid societal costs of food delivery.
• The Labour to make this land productive.
• Using Public transport and avoiding Automobiles that burn fossil fuel (try horse drawn transport...).
For it to work fully, we are talking about reverting to peasant culture in this scenario.
But this is only practical if you have a large site and are near woodland, and don't mind maintaining wood burning stoves and living a peasant lifestyle, not having a job in a city. It is not applicable to 60 million people in an overcrowded island which took decades of smoke control legislation to clean up the air. The World's population has Tripled in my own lifetime. So wood-burning stoves and free range chickens cannot meet that population rise. 1200 houses are due to be built in the field behind our house next year, and the small amount of woodland that is being preserved nearby would be 'scrounged' of free wood within a week.
The 2016 Carbon Zero house target can perhaps only be possible with a co-existing programme of vigorous densification (retaining green belts and more apartments and district heating, and allowing us to have jobs in cities within walking/cycling/bus distance), and vigorous plantations of trees on land not used for agriculture and essential recreation.
If we did the opposite, the US rur-urban solution and dispersed everyone so they had an acre of personal woodland that would not work because of the fire risks (see Los Angeles), but mostly the ginormous societal cost of all the roads and travel costs to reach them... and the unwillingness of most people to live and labour in this way.