Swtich

Tip

• This section provides a detailed description of the switch model implemented in this project. The represents an ideal electrical switch, capable of connecting or disconnecting buses within the power system. It is designed to handle single-phase and multi-phase (e.g., three-phase) systems, each phase operating independently. The primary objective is to accurately model the Switch’s behavior within the Modified Nodal Analysis (MNA) framework, reflecting its open and closed states. *

Mathematical Modeling

Single-Phase Switch Model

The switch is a direct connection between two single buses for a single-phase system. When closed, it effectively creates a short circuit, forcing the voltages at the connected buses to be equal. When open, it acts as an open circuit, allowing arbitrary voltage differences and preventing current flow between the buses.

Three-Phase Switch Model

For multi-phase systems, such as a three-phase system, the switch is designed to manage connections across multiple phases. Each phase of the Switch operates independently, meaning individual phases can be open or closed irrespective of the others. This flexibility allows for the simulation of various scenarios, including phase-specific faults or switching operations. The implementation assumes no mutual coupling between the individual phases of the Switch, simplifying the model while maintaining fidelity for common power system applications.

MNA representation

Unlike passive elements like loads that are characterized by admittance (Y) parameters directly relating current to voltage, an ideal switch in MNA is modeled through constraint equations and auxiliary variables. This approach accurately represents its non-linear, ideal behavior (zero or infinite admittance).

• Close State When a specific phase of the Switch is closed, it imposes an ideal short circuit between its two connected buses, say n1 (with voltage \(V_{n1}\)) and n2 (with voltage \(V_{n2}\)).
  This condition is represented by introducing an auxiliary current variable (\(I_{sw}\)) for that phase and adding the following constraint equation to the MNA system:

\[\begin{equation} V_{n1} - V_{n2} = 0 \end{equation}\]

In the MNA matrix (\(A\)), this equation translates to specific entries: \(A_{\text{row}, V_{n1}} = 1\) and \(A_{\text{row}, V_{n2}} = -1\), where row corresponds to the auxiliary equation for the switch. Furthermore, to account for the current flow, entries are made in the nodal equations for n1 and n2: \(A_{V_{n1}, I_{sw}} = 1\) and \(A_{V_{n2}, I_{sw}} = -1\). The diagonal element \(A_{\text{row}, I_{sw}}\) is set to \(0\) for an ideal switch. This setup effectively models a connection with infinite admittance.

• Open State: When a phase of the switch is , it represents an open circuit. The Switch introduces no constraint or connection between its associated buses in this state. Consequently, no equations or auxiliary variables related to this open phase are added to the MNA matrix. This corresponds to a connection with zero admittance.

Code Explanation

For detailed code information, see the Harmony manual.