Models

Mathematical description of the models implemented in DPsim.

Each page in this section derives one component family: what it represents, the equations that describe it, and what those equations assume. None of them names a class or a file. How a model is arranged in code is in the Developer Guide, and which domains implement which model is in model availability, which is generated from the source and is therefore the authoritative answer to that question.

The domains

A model is written per simulation domain and per phase count, so the same component may exist as a single-phase dynamic phasor model, a three-phase electromagnetic transient model, or both.

EMT carries instantaneous waveforms, DP carries complex envelopes of those waveforms around a carrier frequency, and SP carries steady-state phasors. Ph1 is single phase, usually a positive sequence representation, and Ph3 is three phase. The three domains are not separate methods but cases of one envelope description, which is the subject of dynamic phasors.

The practical consequence is that the domain determines what a model can represent, not only how fast it runs. An envelope domain cannot represent content outside the band it retains, whatever step size is used.

How the models group

Passive elements and branches. RLC elements covers the elements every other model is built from. Branches covers the lines connecting two nodes, including the travelling-wave line. Transformer covers the two-winding transformer and the ideal transformer within it.

Sources, switches and loads. Sources explains why a current source costs nothing while a voltage source extends the system matrix. Switches and loads cover the two-resistance switch and the impedance and current representations of demand. These three share one theme: a choice that looks physical is usually a numerical trade-off.

Machines. Synchronous generator covers the full-order and transient-stability machines, and reduced order the voltage-behind-reactance family from third to sixth order. The regulators that drive them, exciters, turbines and governors, sit alongside.

Converters. Power electronics covers the averaged inverter models, and converter control the phase-locked loop, the oscillator and the cascaded control that distinguish grid-following from grid-forming behaviour.

Interfaces and compensation. SSN components covers components solved simultaneously with the network, the ideal transformer model the general way of splitting a network, and network injection and compensation the representation of the grid beyond the boundary.

Signal blocks. Signal processing covers the integrators, filters and generators the other models are assembled from. These carry no current and connect to no node.


RLC-Elements

Resistance, inductance and capacitance, and the companion models they discretise to.

Branches

Line models connecting two nodes of the network.

Transformer

Two-winding transformer, the ideal part that extends the matrix, and the snubbers.

Ideal Transformer Model

Splitting a circuit at any point with a controlled source pair, and what the delay costs.

Switches

Two-resistance switching and the variable-resistance switch used for faults.

Loads

Constant impedance and constant current representations of a load, and what each assumes.

Sources

Ideal and non-ideal sources, and what each costs the solver.

Network Injection and Compensation

Representing the rest of the grid, and the compensators that regulate voltage against it.

Synchronous Generator

Machine models, from the full dq0 description to the reduced order family.

Synchronous Generator Regulators

Excitation and speed control models attached to the synchronous machine.

Power Electronics

Averaged voltage source inverter models and their control.

Converter Control

Phase tracking, angle generation and the cascaded control that drives a converter.

State-Space Nodal Components

How an individual component is written as a state-space model and turned into a nodal stamp.

Signal Processing Blocks

Integrators, filters and the generators that drive time-varying sources.