# branches

Establish relationship between component Through variables and nodes

Parent Section: component

## Syntax

```branches
a : node1.a -> node2.a;
end

```

## Description

`branches` begins the branches section, which is terminated by an `end` keyword. This section contains one or more branch statements, which establish the relationship between the Through variables of the component and the domain.

For example, a domain declaration contains a Through variable `a`:

```variables(Balancing=true) a = { 0, 'N' } end ```

and a component declares two nodes, `node1` and `node2`, associated with this domain, and a variable `a`:

```variables a = { 0, 'N' }; end```

The name of the component variable does not have to match that of the domain variable, but the units must be commensurate (in this example, `'N'`, `'kg*m/s^2'`, `'lbf'`, and so on).

To establish a connection between the component variable `a` and the domain Through (balancing) variable `a`, write a branch statement, such as:

```branches a : node1.a -> node2.a; end```

`node1.a` and `node2.a` identify the conserving equations on `node1` and `node2`, and the component variable `a` is a term participating in those conserving equations. The branch statement declares that `a` flows from `node1` to `node2`. Therefore, `a` is subtracted from the conserving equation identified by `node1.a`, and `a` is added to the conserving equation identified by `node2.a`.

A component can use each conserving equation identifier multiple times. For example, the component declares the following variables and branches:

```variables a1 = { 0, 'N' } a2 = { 0, 'N' } a3 = { 0, 'N' } end branches a1 : node1.a -> node2.a; a2 : node1.a -> node2.a; a3 : node2.a -> node1.a; end ```

Then, assuming that `node1` and `node2` are not referenced by any other `branch` or `connect` statements, the conserving equations at these nodes are:

• For `node1`

```- a1 - a2 + a3 == 0 ```
• For `node2`

```a1 + a2 - a3 == 0 ```

### Syntax Rules

The following rules apply:

• Each conserving equation belongs to a node associated with a domain. All variables participating in that conserving equation must have commensurate units.

• A node creates one conserving equation for each of the Through (balancing) variables in the associated domain. Branch statements do not create new equations. They add and subtract terms in the existing conserving equations at the nodes.

• The second and third arguments do not need to be associated with the same domain. For example, one can be associated with a gas domain, and the other with a thermal domain, with the heat flow exchange defined by the branch statement.

• You can replace either the second or the third argument with `*` to indicate the reference node. When you use `*`, the variable indicated by the first argument is still added to or subtracted from the equation indicated by the other identifier, but no equation is affected by the `*`.

## Examples

expand all

If a component declaration section contains two electrical nodes, `p` and `n`, and a variable ```i = {0,'A'};``` specifying current, you can establish the following relationship in the `branches` section:

```branches i : p.i -> n.i; end ```

This statement defines current `i` as a Through variable flowing from node `p` to node `n`.

For a grounding component, which has one electrical node `V`, define current `i` as a Through variable flowing from node `V` to the reference node:

```branches i : V.i -> *; end ```

For a mutual inductor or transformer, with primary and secondary windings, the `branches` section must contain two statements, one for each winding:

```branches i1 : p1.i -> n1.i; i2 : p2.i -> n2.i; end ```

For a component such as a constant volume pneumatic chamber, where you need to establish the heat flow exchange between the pneumatic and the thermal domains, the declaration section contains the two nodes and the heat flow variable:

```nodes A = foundation.pneumatic.pneumatic; H = foundation.thermal.thermal; end variables h = { 0 , 'J/s' }; end ```

and the `branches` section establishes the heat flow exchange between the two domains:

```branches h : A.Q -> H.Q; end ```

This statement defines the heat flow `h` as a Through variable flowing from the pneumatic node `A`, associated with the chamber inlet, to the thermal node `H`, associated with the thermal mass of gas in the chamber.

## Version History

Introduced in R2013b