Prediction & Relaxation - State Space Analysis Method

In eHS Gen5, switches introduced a delay in order to support interpolation. There can be one or two delay introduced depending on the solver strategy adopted. Furthermore, to mitigate these latency, a prediction is made on the measurements needed to compute the switches. Coupling of the switches model is done through voltage, and current injection, therefore depending on the stiffness of the circuit, a relaxation need to be applied to the injection to ensure model stability. For switching frequency below 100kHz, prediction and relaxation parameters should be set to the minimum values explained below. 

Solver strategy

Smallest Time Step: This ensures that the circuit will be solved using the smallest time step. For resonating circuit, with high-switching frequency, it will detect current zero-crossing more accurately. As a drawback, there will be two delays solving the switches. Also the time step will be bound between a minimum and a maximum value.

Smallest Latency: This ensures having only 1 delay introduced by the switches. It means that the state-space equations and the switches are solved subsequently. The time step will only have a lower bound.

Prediction

When the option "Smallest Time Step" is chosen, there is a latency of 2 sampling time between switches computation, and measurement coming from eHS. In this case a prediction between 2 and 3.

When the option "Smallest Latency" is chosen, eHS sampling time become bigger, but there is only 1 sampling time between switches computation, and measurement coming from eHS. In this case a prediction between 1 and 2 should yield best results.

Relaxation

This parameter is highly dependent on the circuit topology, and time constant. Its value should be set between 1 and 3. When blocking, a voltage is applied on the AC-side to regulate the AC current to zero. Increasing the relaxation slow down the time it takes to reach steady state. This reduces the stiffness of the model, increase stability. This gain on numerical stability has a drawback of producing reactive power that should not have been present otherwise.

Prediction and relaxation parameters are intended to make the power switches block, or regulate the AC current to zero. They can be compared to PID controller gains. Increasing the Prediction would act as increasing the Integrator gain of the PID controller; if it is too big, it will add overshoot and oscillations, but it should tend toward the reference. Relaxation parameter controls the Proportional and Derivative gain. It is inversely proportional, meaning that increasing the Relaxation would be like decreasing PD gain of a controller. It will take more time to reach steady state, but it will avoid overshoot.