PowerElectronics

Source: GridKit/Model/PowerElectronics/README.md

This sub-directory provides components utilized within the PowerElectronicsModel composer. All components are treated equally and only the composer can view and distribute data to components. Components have no knowledge nor require the existence of any other component. Each component evaluates a set of equations to form residuals. There are two types of variables.

  • Internal Variables \(y\). Variables only need by the component.

  • External Variables \(w\). Variables shared between multiple components.

Each equation is associated to a variable. The residuals generated by external components are assumed to add together to form the final system. Arbitrary amounts of components can be handle and residuals evaluated.

The composer can handle arbitrary components with arbitrary connections. Connections are handled via integer mapping between components and the composer via getNodeConnections and setNodeConnections.

The composer suppose Jacobian constructions as well.

Example with two components is as follows.

Component 1:

\[\begin{split}\begin{align} 0 = f_1\left(\frac{dy_{1}}{dt}, y_1 , w \right) & \qquad \text{(Internal Equations Residual)}\\ c_1(y_1, w) & \qquad \text{(External Coupling Term)}\\ \end{align}\end{split}\]

Component 2:

\[\begin{split}\begin{align} 0 = f_2\left(\frac{dy_{2}}{dt}, y_2 ,w\right) & \qquad \text{(Internal Equations Residual)}\\ c_2(y_2,w) & \qquad \text{(External Coupling Term)}\\ \end{align}\end{split}\]

The composition of components 1 and 2:

\[\begin{split}\begin{align} 0 = f_1\left(\frac{dy_{1}}{dt}, y_1 ,w\right) & \qquad \text{(Internal Equations Residuals)}\\ 0 = f_2\left(\frac{dy_{2}}{dt}, y_2 ,w\right) &\\ 0 = c_1(y_1, w) + c_2(y_2,w) & \qquad \text{(External Coupling Residuals)}\\ \end{align}\end{split}\]

Note the dimensions of \(y\) can be \(0\) if there are no internal equations (an example seen in Resistors and MicrogridBus).