Tech:loadshape

Tech:loadshape - Loadshape technical support document

The basic principle underpinning loadshape is that the total energy $$E$$ consumed by a series of $$N$$ pulses


 * $$E = N P \Delta t \!$$ Eq. 1

where
 * $$P$$ is the power of each pulse
 * $$\Delta t$$ is the duration of each pulse.

At least one of the variables E, N , P , $$\Delta t$$ must remain unspecified by the user in order for Eq. 1 to not be overspecified. Thus


 * $$N = \frac{E}{P \Delta t} \!$$ Eq. 1a

is used to determine the number of pulses,


 * $$\Delta t = \frac{E}{P N} \!$$ Eq. 1b

is used to determine the pulse duration, and


 * $$P = \frac{E}{P \Delta t} \!$$ Eq. 1c

is used to determine the power of each pulse.

In cases where the standard deviation $$\sigma$$ is provided, the power of the pulse is adjusted so that


 * $$P_{adjusted} = Normal[P,\sigma]$$ Eq. 2

Analog loadshapes
When the analog loadshape power $$P$$ is given, the loadshape amplitude $$y_t$$ at the time $$t$$ shall be computed from schedule value $$x_t$$ as


 * $$y_t = P x_t \!$$.

When the analog loadshape energy $$E$$ is given, the loadshape amplitude $$y_t$$ at the time $$t$$ shall be computed from the schedule values $$x_t$$ in the interval $$t=(0,T($$ as


 * $$y_t = \frac{E x_t}{\sum_{t=0}^T x_t \Delta t}$$

where
 * $$\Delta t$$ is the time interval over which the schedule value $$x_t$$ is given.

When neither the energy nor the power are given, the loadshape amplitude $$y_t$$ at the time $$t$$ shall be the schedule value $$x_t$$.

Pulsed shapes
When a pulse loadshape is specified, the power amplitude $$y_t$$ at the time $$t$$ based on the schedule value $$x_t$$ is given by


 * $$y_t = \frac{E}{N \Delta t} x_t$$.

When the energy is not given, the power amplitude may be computed from the power and time interval


 * $$y_t = \frac{P T}{N \Delta t} x_t$$.

When both the energy and power are given, the power amplitude may be computed as


 * $$y_t = \frac{P^2 T}{E}x_t$$

Modulated shapes
describe how modulated shapes are generated from schedules

Queued shapes
describe how queued shapes are generated from schedules

Scheduled shaped
describe how pulse shapes are generated from schedules