# Engineering to Mathematical Data Model Mapping

In this document we define the mapping from the engineering data model down to the mathematical data model for each physical component.

## bus objects

Buses are parsed into bus and potentially shunt objects.

The mathematical bus model contains only lossless connections to ground. All other connections to grounds are converted to equivalent shunts at that bus. For example, take a bus defined as

bus_eng = Dict("grounded"=>[4, 5], "rg"=>[1.0, 0.0], "xg"=>[2.0, 0.0],...).

This is equivalent to a shunt g+im*b = 1/(1.0+im*2.0) connected to terminal 4, and a lossless grounding at terminal 5 (since rg==xg==0.0). This is mapped to

bus_math = Dict("grounded"=>, ...),

shunt_math = Dict("connections"=>, "b"=>[b], "g"=>[g]...).

This simplifies the mathematical model, as the modeller does no longer have to consider lossy groundings explicitly.

## line objects

Lines are parsed into branch objects with transformer=false

## switch objects

Switches are parsed into switch. If there are loss parameters provided (i.e. rs and/or xs) then a virtual branch and virtual bus are created to model the impedance

## transformer objects

A transformer can have N windings, each with its own configuration (delta or wye are supported). This is decomposed to a network of N lossless, two-winding transformers which connect to an internal loss model. The to-winding is always wye-connected, hence we refer to these transformers as 'asymmetric'.

The internal loss model is a function of

• the winding resistance rw,
• the short-circuit reactance xsc,
• the no-load loss properties noloadloss (resistive) and magnetizing current imag (reactive).

If all of these are non-zero, this leads to an internal loss model consisting of N virtual buses, (N^2+N)/2 virtual branches, and 1 shunt. These virtual buses and branches are automatically merged and simplified whenever possible; e.g., when all these loss parameters are zero, this simplifies to a single virtual bus, to which all two-winding transformers connect.

## shunt objects

Shunts are parsed directly into shunt objects.

## load objects

Loads are parsed into load objects. See the discussion under the Load Model documentation on the sidebar, for a detailed discussion of the various load models.

## generator objects

Generators are parsed into gen objects.

## solar objects

Solar objects (photovoltaic systems) are parsed into gen objects.

## voltage_source objects

Voltage sources are parsed into gen objects. If loss parameters are specified (i.e. rs and/or xs) then a virtual bus and branch are created to model the internal impedance.