A power generation system comprising: an engine having a combustion chamber, comprising: a combustion chamber that operates to alternately expand and contract a volume enclosed by the combustion chamber; an intake valve for the combustion chamber controlled to provide an air charge to the combustion chamber volume as that volume is expanding, and controlled to limit the air charge by closing the intake valve before the volume has fully expanded, intake valve being controlled to close with a timing that results in a sub-atmospheric pressure, which is 0.9 atmospheres or less within the volume at the time of full expansion; and a fuel injector controlled to provide a pre-injection of fuel into the combustion chamber volume to mix with the air charge, the pre-injection amount providing the mixture a rich fuel-air ratio, the pre-injection timing being controlled to generate the rich mixture within the combustion chamber before the mixture begins to combust; the controlled air charge and the pre-injection amounts being such that the rich fuel-air mixture will auto-ignite within the combustion chamber as a result of compression caused by contracting the volume, the amounts also being regulated such that the mixture will combust at temperatures that remain below a temperature at which significant amounts of soot would be produced, the combustion chamber thereby being functional to produce an exhaust that is rich and substantially free of NO X and soot; and a solid oxide fuel cell having an air side and a fuel side and configured to receive the engine exhaust on its fuel side and being functional to substantially reduce the chemical energy content of the exhaust while using the chemical energy to produce electrical power. an engine having a combustion chamber, comprising: a combustion chamber that operates to alternately expand and contract a volume enclosed by the combustion chamber; an intake valve for the combustion chamber controlled to provide an air charge to the combustion chamber volume as that volume is expanding, and controlled to limit the air charge by closing the intake valve before the volume has fully expanded, intake valve being controlled to close with a timing that results in a sub-atmospheric pressure, which is 0.9 atmospheres or less within the volume at the time of full expansion; and a fuel injector controlled to provide a pre-injection of fuel into the combustion chamber volume to mix with the air charge, the pre-injection amount providing the mixture a rich fuel-air ratio, the pre-injection timing being controlled to generate the rich mixture within the combustion chamber before the mixture begins to combust; the controlled air charge and the pre-injection amounts being such that the rich fuel-air mixture will auto-ignite within the combustion chamber as a result of compression caused by contracting the volume, the amounts also being regulated such that the mixture will combust at temperatures that remain below a temperature at which significant amounts of soot would be produced, the combustion chamber thereby being functional to produce an exhaust that is rich and substantially free of NO X and soot; and a solid oxide fuel cell having an air side and a fuel side and configured to receive the engine exhaust on its fuel side and being functional to substantially reduce the chemical energy content of the exhaust while using the chemical energy to produce electrical power. a combustion chamber that operates to alternately expand and contract a volume enclosed by the combustion chamber; an intake valve for the combustion chamber controlled to provide an air charge to the combustion chamber volume as that volume is expanding, and controlled to limit the air charge by closing the intake valve before the volume has fully expanded, intake valve being controlled to close with a timing that results in a sub-atmospheric pressure, which is 0.9 atmospheres or less within the volume at the time of full expansion; and a fuel injector controlled to provide a pre-injection of fuel into the combustion chamber volume to mix with the air charge, the pre-injection amount providing the mixture a rich fuel-air ratio, the pre-injection timing being controlled to generate the rich mixture within the combustion chamber before the mixture begins to combust; the controlled air charge and the pre-injection amounts being such that the rich fuel-air mixture will auto-ignite within the combustion chamber as a result of compression caused by contracting the volume, the amounts also being regulated such that the mixture will combust at temperatures that remain below a temperature at which significant amounts of soot would be produced, the combustion chamber thereby being functional to produce an exhaust that is rich and substantially free of NO X and soot; and a solid oxide fuel cell having an air side and a fuel side and configured to receive the engine exhaust on its fuel side and being functional to substantially reduce the chemical energy content of the exhaust while using the chemical energy to produce electrical power.