# Substation Sag Algorithm

The Substation Sag lgorithm allows you to apply a sag to a variable cable object. You have the ability to specify the amount of sag, weight per unit length of the cable, bend radius of the cable, offset, and how many points to plot. Specifying these values will allow you to create a catenary for a level or inclined span.

## Catenaries

The catenary is the curve that an idealized hanging chain or cable assumes when supported at its ends and acted on only by its own weight. The curve is the graph of the hyperbolic cosine function and is similar in appearance to a parabola. If a bend radius and/or an offset are defined, the catenary will get drawn starting at their end points. If both do not exist, the catenary will connect directly to the supports.

## Level Span

A level span means that the two supports the cable is attached to are at the same height. The middle of the cable will be at the lowest point. The distance between the support and the lowest point is known as the conductor sag. When sag is involved, the cable will need to be longer than the distance between the supports. The length of the cable is referred to as the stressed arc length.

 S The amount the conductor sags. L The stressed arc length. A The distance between the two supports.

## Inclined Span

An inclined span means that the two supports the cable is attached to are different heights. The conductor sag for an inclined span is the vertical distance between a line joining two supports and a point on the conductor with the same slope as the line. Since the two supports have different heights, the lowest point on the conductor may no longer be in the middle.

 S The amount the conductor sags. It is the vertical distance between an imaginary line joining two supports and a point on the conductor with the same slope, B/A, as the imaginary line. L The stressed arch length. A The distance between the two supports. B The difference in elevation of the supports. C The distance of an imaginary line joining the two supports. X1 The horizontal distance from support 1 to the lowest point of the conductor. X2 The horizontal distance from support 2 to the lowest point of the conductor. Y1 The vertical distance from support 1 to the lowest point of the conductor. Y2 The vertical distance from support 2 to the lowest point of the conductor.

A cable may need to get bent if it passes by or through structural elements where an edge may touch the cable. A cable can only bend a specific amount before internal or external damage may occur. This amount is known as the minimum bending radius of a cable. Based on the type of cable used, the bend radius will vary. If an offset is defined, the bend radius will get drawn starting at the end of the offset. If it does not exist, the bend radius will connect directly to the supports.

To illustrate a bend radius, imagine a circle whose diameter hugs onto the curve of the cable. The bend radius will be equivalent to the radius of the circle. The image above shows a cable being bent around a radius of 5 inches. The minimum bending radius is usually a multiple of the cable's diameter.

## Using the Algorithm

After a variable cable object has been selected in the Insert Substation Objects dialog, the Cable/Bus Object Settings Dialog displays. In the Sag Options section select Catenary Sag and enter values for the required parameters used by the algorithm.

SettingDescription
Sag The amount you want the conductor to sag. The units of sag are defined by the DGN master units. The cable symbol's settings should also match this unit.
Weight The weight of the conductor per unit length. The unit of weight for an imperial design is lb and kg for a metric design. The units of length are defined by the DGN master units. The cable symbol's settings should also match this unit.
Bend Radius The amount the conductor will get bent at each support. The units of measurement are defined by the DGN master units. The cable symbol's settings should also match this unit.
Offset This will draw a line following the direction of the hook point attached to a support for the length specified. The units of length are defined by the DGN master units. The cable symbol's settings should also match this unit.
Points The number of points to plot. The more points you plot, the smoother the line will appear. The starting, ending, and offset points are not counted towards the total number of points to plot.
Update Reads in the parameters, calculates the plot points, and plots the variable object. The dialog will remain open so changes can be made if incorrect parameters where used. If clicked again, the plotted variable object will get deleted, the plot points will get recalculated, and a new variable object will get plotted.
OK Reads in the parameters, calculates the plot points, closes the dialog, and plots the variable object.
Cancel Discards any parameters set and closes the dialog.

## Created Variable Object

After a variable object has been created using the Substation Sag algorithm, you can select it, right click, and choose Device ID... to open the Device Properties dialog. The quantity listed for the part number will be the length of the entire object.

Also, if you move the starting or ending supports the variable object will automatically get redrawn using the same parameters. The length will also get updated.