# Diversity factor

Diversity factor (or simultaneity factor $k_\text{s}$) is a measure of the probability that a particular piece of equipment will turn on coincidentally to another piece of equipment. For aggregate systems it is defined as the ratio of the sum of the individual non-coincident maximum loads of various subdivisions of the system to the maximum demand of the complete system.

$f_{Diversity} = \frac{ \sum\limits_{i=1}^n\text{Max}(\text{Load}_i)}{\sum\limits_{i=1}^n\text{Load}_i}$

The diversity factor is almost always less than 1 since all components would have to be on simultaneously at full load for it to be one. The aggregate load $\left( \sum\limits_{i=1}^n\text{Load}_i \right)$ is time dependent as well as being dependent upon equipment characteristics. The diversity factor recognizes that the whole load does not equal the sum of its parts due to this time interdependence (i.e. diverseness). For example, we might have ten air conditioning units that are 20 tons each at a facility. In Florida we typically assume that the average full load equivalent operating hours for the units are 2000 hours per year. However, since the units are each thermostatically controlled, we do not know exactly when each unit turns on. If the ten units are substantially bigger than the facility's actual peak A/C load, then fewer than all ten units will likely come on at once. Thus, even though each unit runs a total of 2000 hours a year, they do not all come on at the same time to affect the facility's peak load. The diversity factor gives us a correction factor to use, which results in a lower total kW load for the ten A/C units. If the energy balance we do for this facility comes out within reason, but the demand balance shows far too many kW for the peak load, then we can use the diversity factor to bring the kW into line with the facility's true peak load. The diversity factor does not affect the kWh; it only affects the kW.

## Coincidence factor

The coincidence factor is the reciprocal of the diversity factor. However, differing sources define the simultaneity factor to be identical to either the coincidence factor or the diversity factor. The International Electrotechnical Commission defines the coincidence and simultaneity factors identically with the diversity factor being the reciprocal. Since the only change in definition is to take the inverse, all one needs to know is if the factor is greater than or less than one.

## Diversity

The (unofficial) term diversity, as distinguished from diversity factor refers to the percent of time available that a machine, piece of equipment, or facility has its maximum or nominal load or demand (a 70% diversity means that the device in question operates at its nominal or maximum load level 70% of the time that it is connected and turned on).

## Diversified load and diversification factor

The diversified load is the total expected load (power) to be drawn during a peak period by a device or system of devices. The diversified load is the combination of each devices full load capacity, Utilization Factor, Diversity Factor, Demand Factor and the Load factor(electrical)|load factor. This process is referred to as load diversification. The diversification factor is then defined as:

$f_{Diversification} = \frac{\text{Diversified Load}}{\text{Maximum system load}}$

## In mathematics

Diversity factor is commonly used for a number of mathematics-related topics. One such instance is when completing a coordination study for a system. This diversity factor is used to estimate the load of a particular node in the system.