How to increase station storage?

I have super large station in a city of 175,000, so coverage of station is fully covered by buildings. But I never seen more than 1,500 passengers in my station. That's bad, because if some Airbus A380 land on the linked airport, they will totally drain my station. I made some feeder services by buses, but passengers from there won't remain longer than couple of seconds and I still only have around 1,500.

Is there any way to "store" more passengers in station?

In general, you don't want to do this. Having 1500+ units of cargo waiting at a station means you're losing a third or more of your potential station rating (and thus, cargo generation). Instead, you want to increase your rate of flow, both in and out, so that vehicles will load quickly and completely even without cargo waiting.

That said, there are ways of doing this.

• The easiest is to have feeder routes. Cargo deposited in a station to be moved onwards by another vehicle tends to stick around for a while. Make sure that your feeder vehicles use the instruction "transfer and leave empty", otherwise they'll pick up the cargo they just dropped off.
• The harder option is to increase the rate of cargo generation. For industries, this means placing a station where it can accept cargo from more than one industry of a given type (eg. two coal mines within a rail station's coverage can generate cargo fast enough to have 1500+ waiting, as could a steel mill fed by a dozen iron mines). For passengers/mail, you can connect a station component with a high radius (eg. a bus station with a radius of 3 connected to an international airport with its radius of 10 will get all the passengers and mail from within the airport's coverage area).
• The cheap option is to play games with the rules for catchment areas. Place disconnected station components (say, drive-through bus stops or loading bays) strategically around the actual station to give it a much larger catchment area (and thus, rate of cargo generation) than it normally would have.

another way to increase the cargo stored in the station is by increasing the rating of the station. The easiest way to do this is by placing the station in an advertisement area and advertise regulary. This is a lot of work but there are some openttd clients available which can do this automatically for you. here you can find how stationrating is calculated: https://wiki.openttd.org/Game_mechanics

I already read some people answered about a lot of busstop to increase catchment area. Another way to do this is by adding tiles with a bigger catchment area to the station. All tiles of the station will get this catchmentarea. See the following link: http://wiki.citymania.org/index.php?title=Enlarge_catchment_area(trick)

here I found an external link how to store 33k of goods in a station: http://wiki.citymania.org/index.php?title=Quest:IKEA this in general holds for any cargo you want to have in a station.