I did a small project with arduino to control and monitor an aquarium. I have powered that from a small 9V dc power supply. It is a AC 230V to DC 9V converter.
I need the system to run every time (24h x7 x365 
) . So I need some backup power supply like a battery besides that 9V power supply. So it would work from that backup power source in case of a power failure.
Please suggest me some ideas for this.
Get a USB battery pack. Plug your Arduino into the battery and then battery into your wall. When power is lost, the battery will power the Arduino.
Thank you for the reply. But I have 8 relays. So a battery pack won't last long. I am afraid I can change the battery inside a battery pack. I can buy any battery. I am looking for something more advanced and reliable so I do not have to worry about my fish.
Convert solution to use latching relays
sahirudilan:
So a battery pack won't last long.
Get a big one. Like this one: http://www.mi.com/en/pb10400/. It's what I use for my Gopro when doing multi-day time lapses. I get long operation life and back-up if there is an issue with mains power.
sahirudilan:
I can buy any battery.
Battery packs contain batteries.
sahirudilan:
I am looking for something more advanced and reliable so I do not have to worry about my fish.
More advanced in what way? Or you want something more complicated and less reliable?
You provided no details in your original post. Other than "small 9v supply." What is "small"? How much current does your design draw? How long do you want it to last? Why wouldn't 10400mAh be enough?
I actually didn't measure it yet. I have used the power banks and I do not like them mush. 
May be I tried the cheap ones. I will find a better one. Thank you sir.
So you have a multi-relay solution and you don't wish it stopping working right... I might ask what's being controlled by those relays? It must be something "big" to be using relays correct? How the power backup works for that? If you already have something in place, can't you borrow energy from it?
Anyway, if you don't have backup for controller neither the load, the most transparent way would be buying a proper UPS, like the APC ones, those are quit good. You might decide to plug your load on it, because if you're controlling something that depends on mains and the mains goes down, your biggest problem is the "load" and not the controller.
Using an USB power pack might work for the controller, but I haven't see one designed to keep charging and connected to the load at the same time. If you fully charge one and connect to your controller you might have a bad experience if you forget to recharge it frequently - also you will have a time without backup while charging it (or at least a few seconds disconnecting one and connecting a charged USB power pack).
Buy a regular UPS backup system from reputed manufacturers.