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Tech:loadshape - Loadshape technical support document

The basic principle underpinning loadshape is that the total energy <math>E</math> consumed by a series of <math>N</math> pulses

<math>E = N P \Delta t \!</math>
Eq. 1

where

  • <math>P</math> is the power of each pulse
  • <math>\Delta t</math> is the duration of each pulse.

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

<math>N = \frac{E}{P \Delta t} \!</math>
Eq. 1a

is used to determine the number of pulses,

<math>\Delta t = \frac{E}{P N} \!</math>
Eq. 1b

is used to determine the pulse duration, and

<math>P = \frac{E}{P \Delta t} \!</math>
Eq. 1c

is used to determine the power of each pulse.

In cases where the standard deviation <math>\sigma</math> is provided, the power of the pulse is adjusted so that

<math>P_{adjusted} = Normal[P,\sigma]</math>
Eq. 2

Analog loadshapes

When the analog loadshape power <math>P</math> is given, the loadshape amplitude <math>y_t</math> at the time <math>t</math> shall be computed from schedule value <math>x_t</math> as

<math>y_t = P x_t \!</math>.

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

<math>y_t = \frac{E x_t}{\sum_{t=0}^T x_t \Delta t}</math>

where

  • <math>\Delta t</math> is the time interval over which the schedule value <math>x_t</math> is given.

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

Pulsed shapes

When a pulse loadshape is specified, the power amplitude <math>y_t</math> at the time <math>t</math> based on the schedule value <math>x_t</math> is given by

<math>y_t = \frac{E}{N \Delta t} x_t</math>.

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

<math>y_t = \frac{P T}{N \Delta t} x_t</math>.

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

<math>y_t = \frac{P^2 T}{E}x_t</math>

Modulated shapes

 TODO:  describe how modulated shapes are generated from schedules

Queued shapes

 TODO:  describe how queued shapes are generated from schedules

Scheduled shaped

 TODO:  describe how pulse shapes are generated from schedules

See also