Per-unit Conventions

It is often useful to express power systems data in relative terms using per-unit (p.u.) conventions. PowerSystems.jl supports the automatic conversion of data between three different unit systems:

1. "NATURAL_UNITS": The naturally defined units of each parameter (typically MW).
2. "SYSTEM_BASE": Parameter values are divided by the system base_power.
3. "DEVICE_BASE": Parameter values are divided by the device base_power.

PowerSystems.jl supports these unit systems because different power system tools and data sets use different units systems by convention, such as:

• Dynamics data is often defined in device base
• Network data (e.g., reactance, resistance) is often defined in system base
• Production cost modeling data is often gathered from variety of data sources, which are typically defined in natural units

These three unit bases allow easy conversion between unit systems. This allows PowerSystems.jl users to input data in the formats they have available, as well as view data in the unit system that is most intuitive to them.

You can get and set the unit system setting of a System with get_units_base and set_units_base_system!. To support a less stateful style of programming, PowerSystems.jl provides the Logging.with_logger-inspired "context manager"-type function with_units_base, which sets the unit system to a particular value, performs some action, then automatically sets the unit system back to its previous value. For a worked example of switching unit systems and reading component values, see Read Component Values in Different Unit Systems.

Conversion between unit systems does not change the stored parameter values. Instead, unit system conversions are made when accessing parameters using the getter functions, thus making it imperative to utilize the getter functions instead of the "dot" accessor methods to ensure the return of the correct values. The units of the parameter values stored in each struct are defined in src/descriptors/power_system_structs.json.

There are some unit system conventions in PowerSystems.jl when defining new components. Currently, when you define components that aren't attached to a System, you must define all fields in "DEVICE_BASE", except for certain components that don't have their own base_power rating, such as Lines, where the rating must be defined in "SYSTEM_BASE".

In the future, PowerSystems.jl hopes to support defining components in natural units. For now, if you want to define data in natural units, you must first set the system units to "NATURAL_UNITS", define an empty component, and then use the getter functions (e.g., getters and setters), to define each field within the component. The getter functions will then do the data conversion from your input data in natural units (e.g., MW or MVA) to per-unit.

By default, PowerSystems.jl uses "SYSTEM_BASE" because many optimization problems won't converge when using natural units. If you change the unit setting, it's suggested that you switch back to "SYSTEM_BASE" before solving an optimization problem (for example in PowerSimulations.jl).

Transformer per unit transformations

Per-unit conventions with transformers simplify calculations by normalizing all quantities (voltage, current, power, impedance) to a common base. This effectively "retains" the ideal transformer from the circuit diagram because the per-unit impedance of a transformer remains the same when referred from one side to the other. A more in-depth explanation can be found in this link or basic power systems literature.

Transformer impedance (usually reactive impedance, $X_{pu}$) is typically given on the transformer's own nameplate ratings (rated MVA and rated voltages). The data in PowerSystems.jl is stored on the device base and converted to the system base when using the getter functions.

The key quantity needed for that conversion is the base impedance of each voltage zone:

\[Z_{base} = \frac{(V_{base,\,LL})^2}{S_{base,\,3\phi}}\]

with $V_{base,\,LL}$ in kV and $S_{base,\,3\phi}$ in MVA. The zone base voltage is propagated from the primary side using the transformer's turns ratio:

\[V_{base,\,\text{secondary}} = V_{base,\,\text{primary}} \times \frac{V_{\text{rated,\,secondary}}}{V_{\text{rated,\,primary}}}\]

Note that this value can differ slightly from the attached bus voltage set point. As of PowerSystems.jl v5, transformer components carry an explicit field for their base voltage to make this relationship unambiguous.

For a step-by-step guide to establishing base values and performing the impedance base change manually, see Convert Transformer Impedances Between Per-Unit Bases.