Twenty-nine investors from Europe and the Middle East contributed $2.15bn to the total over the past year-and-a-half.
The Tokyo-based asset manager has secured $176m of commitments from a group of domestic investors for the new green vehicle.
The two UK-focused funds could potentially raise nearly £3bn if hard-caps are met.
The Montreal-based firm is expecting low-teen returns for its inaugural infra fund, targeting North and South American assets.
The firm is looking to close its second series of fundraising on €1.1bn early next year.
The clean lender is looking for an advisor and placement agent as it gears up to raise and manage third-party capital.
The manager will hold its next close by 15 December on more than $6.5bn, with its second fund one deal away from being fully deployed.
The fund, which has made three investments to date, also exceeded its hard-cap by $24m.
The vehicle, now officially launched, could raise up to £500m and comes after the firm has committed more than £1bn to UK projects.
The firm’s strategy is aiming to provide an IRR of between 16% and 20% from investments in up to 15 projects.
The country’s debut core infra fund is targeting $450m, with about three-quarters to be raised at first close.
The firm is investing more than $60m in an 84MW portfolio of gas-fired projects to be developed in England and Wales.
The fund’s £1bn predecessor is exhibiting a 20.6% return in the three years since it closed, reveals the insurer.
The investment includes $600m into the firm’s third fund, which reached a first close of more than $5bn last month.
The firm’s second infra fund, fresh from a $4bn-plus first close, is looking to end fundraising during the first quarter of next year.