10.3.1.5 Matching (instantaneous) power with (aggregate) energy consumed in time

A very common opex element of network equipment models is power consumption. Typically a multiplier transformation is used to determine the (instantaneous) power consumption per unit of a given resource (such as a switch or router or whatever). In earlier versions of STEM, the only viable approach was to define an associated Power resource with (persistent) capacity of (say) 1kW. Its unit cost would have to be defined as the cost of providing 1kW non-stop for a year (which would then be billed in proportion to the length of each period and the utilisation in that period).

Given the introduction of the consumable resource in STEM 7.3, it is obviously preferable to have an Energy resource with (consumable) capacity of (say) 1kWh. Its unit cost would then be defined directly as the cost per kWh. However, according to the strict separation suggested so far, you would have to first use a Time Factor transformation to calculate the (aggregate) required energy each period in kWh before mapping this onto the actual Energy resource.

It is intuitive to think of the ‘h’ in kWh is an attribute of the capacity, rather than the demand, and to this end an optional Capacity Period can be defined for a consumable resource which tells STEM ‘how long its capacity lasts’. In other words, its consumable capacity corresponds to some kind of instantaneous measure (power) sustained for a specific period of time (an hour). This time-dependent behaviour is enabled by setting an associated Time Factor input to Yes as an explicit opt-in.

Figure 1: Mapping an instantaneous Power demand to an in-time consumable Energy resource

The instantaneous demand must be scaled by the length of current period as a multiple of the length of the Capacity Period in order to infer the effective aggregate demand for the consumable resource in kWh; e.g., kW × (hours per current period). This aggregate demand is then divided into the nominal capacity in kWh in order to calculate the number of billing units consumed in the current period. The calculations are exactly as if the Time Factor transformation suggested above were incorporated into the resource.

The Energy resource is still consumable in the sense that its capacity is used up and is aggregated across periods when consolidated in the results, but we shall refer to it as an in-time consumable resource to reflect the implicit time factor which allows it to be driven by an instantaneous demand.

Matching (aggregate) hours required to (persistent) engineer capacity per week

Just like the Time Factor transformation, there is an inverse case in which a Capacity Period can be used to allow a persistent resource to be driven by an aggregate demand. Recall the conversion from aggregate to instantaneous which we did to compare contracted aggregate maintenance costs with instantaneous capacity of salaried engineers.

If you have an aggregate demand of hours required for maintenance tasks, you could map this directly to a persistent Engineer resource with a capacity of tasks per month or more generally with a capacity of hours per week (or whatever). The subtlety here is that it is not the aggregate tasks or hours which are factored, but the ‘per week’ or ‘per month’ part. (Note it is per week as opposed to for an hour as per the energy example.)

Figure 2: Mapping an aggregate Tasks demand to a per-time persistent Engineer resource

The aggregate demand must be divided by the length of the current period as a multiple of the length of the Capacity Period in order to infer the effective instantaneous demand for the persistent resource in tasks or hours per week; e.g., tasks or hours / (weeks per current period). Then this instantaneous demand is divided into the nominal capacity in tasks or hours per week in order to calculate the number of engineers required in the current period. Again the calculations are exactly as if an inverse Time Factor transformation (Output Mode = Instantaneous Rate) were built into the resource.

The Engineer resource is still persistent in the sense that its instantaneous capacity of tasks or hours per week is ongoing, rather than being used up. When consolidated in the results, we take the last period value for Used Capacity. We shall refer to it as a per-time persistent resource to reflect the implicit time factor which allows it to be driven by an aggregate demand.

These classifications and dynamics are compared more succinctly in the table below:

Figure 3: Comparing resource capacity modes and periods for instantaneous and aggregate demands

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