eHS Solver Theory
The eHS Solver uses Modified Nodal Analysis to generate a conductance matrix that, when solved, returns the voltage at each node of the circuit and the current in each branch. The conductance matrix of the circuit is generated independently from the state of the switches, and therefore does not need to be recomputed when a switch is opened or closed during the simulation. This is achieved through the implementation of the Pejovic method, which represents each Switch component as an impedance–a conducting switch is represented as an inductor and an open switch is represented as a capacitor.
The inductors and capacitors are further simplified using Backwards Euler discretization, and their equivalent circuits become a current source with a shunt resistance.
For the conductance matrix to remain constant throughout switching events, the following equations, which define the Switch Conductance (Gs), must remain true.
where h is the simulation time step of the circuit. When building the nodal matrix, Gs is defined for each switch, typically within a range of 0.001 to 10. It determines the value of the inductance and the capacitor representing the switch in conducting and non-conducting states.
For example, for a time step of 100 ns and a Gs of 1, the switch will be represented by the following inductance and capacitance:
The Gs value for each switch is dependent on the following factors:
- Topology of the circuit
- Circuit parameters including Base Power, Source Current(s), Source Voltage(s), Duty Cycle, Load Current(s), Load Voltage(s)
Typically, a good approximation for Gs is:
where Imax is the maximum current flowing outside the converter and Vmax is the maximum voltage at the arm middle point. For example, in the Two Level Arm circuit below, Imax is 64A (signal Y02_Iac) and Vmax is 100V (signal Y01_Vac), therefore the optimal value for Gs is 0.64.
Sample Gs Values
See the table below for a sample list of recommended Gs values for a Two-level NPC Inverter with RL Load and Back EMF (single phase or three-phase).
|DC Source Voltage (V)||Load Current RMS (A)||Gs|
For additional assistance tuning the Gs values, please contact OPAL-RT Technical Support.