The parable of the frog and boiling water is hundreds of years old. It has been used throughout history as a metaphor for circumstances in life when people are unable to see gradual change around them.
AZ Dept. of Commerce Report  Sizing a Photovoltaic System
Sizing a Photovoltaic System
(What follows is a quick and easy method for sizing photovoltaic systems. However, the formula is not intended
to be a sizing procedure for design purposes, but is offered only as an aid to readers seeking preliminary sizing information. For accuracy in system design, the guidance of an experienced photovoltaic system designer is highly recommended.)
The size, and subsequently the cost, of a photovoltaic system depend upon two factors: the electrical requirements of the devices (loads) relying on the system and the amount of sunshine available to power the system. Both factors determine the quantity and size of panels, batteries, and other components.

The Load
The load is defined as the amount of electric power being consumed at any given moment. To determine the load, it is necessary to select the units that will rely on the system for power. If the system is used to power a home, the load will consist of appliances, lights and other common home items.
The next step is to determine the wattage of each item. The wattage of a device is usually stamped or printed on a nameplate or identification plate on the rear of the unit. If the unit lists VA (volts x amps), that is the wattage. If only amps are listed, multiply the amps by the volts listed to find the wattage.
Finally, decide how many hours per day (average) each item is to be used. The load estimate must be as precise as possible to avoid oversizing or undersizing the system. If design is oversized, money is wasted on excess capacity. If it is undersized, power shortages during operation may result.
The average daily load then, is found by the following formula:
Daily load = wattage X time in use (DL = W x T) DL = 100 watts x 2 hours DL = 200 watthours
The load profile, together with the amount of sunshine, can be used to determine the size of the array.

Available Sunshine
Sunshine is rated in peak hours, the hours of the day at which you can expect the maximum rated performance from a solar panel. On average, Arizona has six peak hours of sun daily.
Panels are rated in peak watts, the amount of electricity they can produce at peak sun. Consequently, the number of watthours available from a panel is found by this formula:
Panel Number hours peak sun
Watthours = x rated panel output
(Wh = Sp x P)
Wh = 6 hours x 40 watts
Wh = 240 watthours per panel
Size of the Array
Because batteries and inverters consume a certain amount of the power generated by the solar cells, it is wise to allow for at least a 20 percent safety factor over and above the exact calculated load needs.
The number of panels is thus calculated as follows:
number of panels = 
(Daily load x 1.2) 
needed 
Watthours 
Number of Batteries
To determine the number of batteries required for the daily load, the owner must decide how many days of reserve he or she desires. Storage batteries must be capable of operating the load during periods of little or no sun, without any electricity generated by the photovoltaic array. (A PV system that requires one to five days’ storage capacity should be outfitted with special, deepcycle batteries.)
To determine the number of batteries required, the designer must know how much energy the batteries can store (energy capacity) and compare that to the daily load and desired reserve. Batteries are normally rated in amphours instead of watthours. To convert to watthours, use the following formula. (Battery capacity and discharge average voltage are usually stamped on the battery)
Battery Daily load (watthours) x Capacity = discharge average voltage in watt hours
Once the battery capacity is knows, the number of batteries required can be calculated from the figures previously determined as follows:
Number Batteries= 
Watthours Days required x reserve 

needed 
Energy capacity (watthours) per battery 
