Use only electricity that is generated by solar panels and what is stored in the

There are a multitude of inverters.
It depends largely on each particular inverter.

There are, what is known as, inverter/chargers that allow grid power to pass through while charging a battery bank, even while the bank is also receiving a charge from other sources. In the event of a blackout or if you where to just turn the circuit off the is supplying grid power to the inverter, it transfers to battery power to make vac automatically, even if the bank is receiving a charge from other sources. An example of this one is the Trace DR1512. 1500 watts continuous, 120 vac modified sinewave output, 12 vdc nominal input (or 24 vdc input - the 1524). I should point out that it will also operate from a vac generator.

Do you have a particular inverter in mind and what types of load(s) will it power ie; sensitive electronics such sound equipment or, resistive loads such as electric heat and incandescent lighting or, reactive loads such as vac motor and florescent lighting and transformers?

Could the load(s) be powered by vdc instead? Eliminating the inverter inefficiencies.

A word about sinusoidal wave forms. Pure sinusoidal wave form can only come from a spinning force. Its three dimensional. Imagine looking at a stretched out Slinky from one end. What you are probably used to seeing is a two dimensional representation of this as a smooth flowing curved wave going up and down. These low vdc to a higher vac inverters, very basically, turn the low vdc off and on so that it can be stepped up to higher vac by way of a transformer. Similar to a coil in an automobile ignition system. The points open the 12 vdc to the coil which causes the magnetic field on one set of windings in the coil to colapse and be induced on another set of windings in the coil that step up the voltage which goes to the spark plug where it shorts out with a high intensity arc.

Square wave - pretty much obsolete, best used for resistive loads. As the name implies, straight over, straight up, straight over and, straight down.

Modified sine wave - (another way of saying modified-square wave) good for most household needs but not so good for sensitive electronics or possibly some sound equipment. Imagine steps going up and down instead of squared over, up, over and, down.

True sine wave - (another way of saying ultra-modified square wave) good for almost everthing depending on the quality of its materials and manufacture, which is true for all manmade products. Many more steps up and down.

More fun with wavelengths;
http://imagine.gsfc.nasa.gov/docs/science/know_l1/emspectrum.html
http://micro.magnet.fsu.edu/electromag/java/index.html
http://www.music.sc.edu/fs/bain/atmi02/wt/sine/index.html

I think I understand what you're saying, but you might want to consider a different approach.  Basically, you want to consume more than your system is capable of providing.  Consider an AC transfer switch (either automatic or manual).  Once you've used as much power from the batteries as you dare to use, turn off the inverter.  The transfer switch switches to grid power.  To protect your batteries, allow them to fully charge again before switching the inverter on.  The entire process can be automated, if you wish.  That is how my system is set up.