There are several reasons why your alternator may be throwing its belt under hard acceleration. You may be effected by one or a combination of the following problems.

1.) When force is applied to your belt by the crank pulley, it creates a little loop in the belt. This is where the belt gets stretched a tiny bit. The more force you apply, the greater this loop can be.
   This loop has two effects on your system. The first thing it does is spin the freest spinning pulley extremely fast. In the modern serpentine systems this is the tension arm pulley. When the tension arm fails it usually becomes the alternator’s pulley. This will cause the alternator’s front bearing to fail prematurely. It is estimated that 40% of all vehicles in America have a bad tension arm on them.
   This loop in extreme cases can also cause the belt to jump right off the pulley. Though this usually only happens in combination with another problem, as described below. The solution to this problem is to install a tension arm pulley, as found on most modern automobiles. Besides absorbing the loop it will also keep the proper tension in the belt system.
   Don’t think that is a big deal? Lift the hood on any modern car and look at the tension arm. If it is functioning properly it will be moving up and down rapidly. What is causing this? All the components are bolted securely to each other, so it has to be the belt getting longer and shorter.
   On the older “V” belt systems the easy fix is to add a deep grove pulley. This reduces the chance of the loop being able to jump over the edge of the pulley. It is a workable solution, but does not have the added benefits of the tension arm.
   A large alternator pulley will also help with this. But there are several other factors to consider before doing this. Check are articles on Pulley ratio and .System Voltage

2.) Original equipment alternator’s mounting brackets were designed for use in small HP motors, with relatively low output alternators. When you increase the output of the alternator, you increase the HP requirements to turn it. Therefore a greater amount of power has to be transferred from the crank pulley to belt to the alternator pulley. Since your higher output motor has more HP, it can do this easily.
   But what happens is the alternator’s body and mounting brackets are having a far greater force applied to them. This can and often does, cause the alternator to twist in the bracket, or flex the bracket altogether.
   When this happens the alternator and crank pulleys become misaligned and the belt flies off. To correct this problem, make sure first the alternator is snug in the bracket and then you may also have to reinforce the bracket itself. Adding a bracket to the rear of the alternator will also help greatly.

3.) If your alternator and crank pulleys are not aligned properly, the belt will stay on with gradual rpm changes. But when you stomp on the gas hard, the belt will fly off. So it is critical that you have the pulleys in alignment within a 1/16 of an inch of each other.
   There are laser pulley alignment tools now available, and they are perfect for the job. If there is room you can also use a true straight edge to check for alignment as well.
   It is also important to ensure that the pulleys are rotating on the same plane. It is possible for the bottom edge of the pulleys to be in alignment but not the top edge. For safe operating both top and bottom edges have to be in alignment.
   If your pulleys are not properly aligned, nothing you do will solve your problem until this is corrected first.

   We find in most cases it is actually a combination of the above three problems that cause the belt to fly off. If you are experiencing this problem, first check your pulley alignment, then your alternator for twisting under load, and after that add either a deep grove pulley or tension arm, or both for that matter.