By a dehumidifier salesman/avocate:
A properly set-up a/c will control the humidity provided to can operate +12 hours a day. Typically, when a/c removes 100 pints/lbs of moisture a day and it maintains <50%RH. The amount of moisture removed is about 2 pints per KW. The more sofisticated a/cs are able to remove the 100 pints with less operating time. A test by a major a/c mfg. indicates 20-30% less cooling load reqired to remove the 100 pints of moisture per day. The pints/KW are less than 2 pints/kw. The multispeed complex controled systems may require the equivalent of 8 hours of full sized a/c operation to remove the 100 pints of moisture. The next option is to over-cool the building to remove more moisture. Overcooling is much more costly and presents many more problems. Comfort, condensation in exterior walls/insulation, condesation on ducts/grills, and lower pints per KW are some of the problems. Clearly, on 65^-70^F rainy day, this is not an acceptable option. In the current mold sensitive culture, over-cooling is not a viable option.
A high efficiency dehumidifier connected to a properly set-up a/c works as follows. The dehumidifier does not preform any function during the +12 hour a/c day. As the operating hours of the a/c decrease, the dehumidifier picks of the load at 5 pints per KW plus adding 1,300 btus per pint removed of heat back to the home. This considered free reheat and as the a/c removes the heat, the a/c also removes moisture. The warm air from the dehu also helps dryout the a/c ducts. During wet cool weather the dehumidifier controls moisture @ 5 pints per KW and providing 8,000 btus per KW of heat. This is a great heat pump. Unfortunately, the time in most climates when this a significant benefit is to short. As the outside dew points go below 50^F, the need for dehumdification ceases and adequate ventilation with dry outside air meets the need.
Also, the whole house dehumdifier works well with fresh air ventilation, being able to blend the fresh air with house air, filtering both, dehumidifying both when wet, and distributing the blend throughout the home. A major difference between whole whouse dehumdification is the ability to control indoor humidity with no a/c operation during warm weather. Maintaining <50% RH while the a/c is set-up for extended periods of times allows t-stat set-up for energy conservation without danger of high moisture anyplace in the structure. In addition, slight oversizing of the a/c only means the dehumdifier will operate a little more. Dehus are overal better than more the complex a/c regarding energy, comfort, and simplicity(long term maintainance). Thanks for a great question. TB