# PHIL bandwidth and stability

Determining the amplifier bandwidth is a factor not to be underestimated in determining the total PHIL system cost. In fact, the total system cost can double if high-frequency amplifiers are required compared to a normal low-frequency amplifier.

**Emulating motors**

Example: we want to simulate a motor to test the thermal capacity of an inverter design. For this, it suffices to emulate a simple motor model capable of reproducing the RMS value of the motor current under various conditions such as steady-state and overload. A low-frequency amplifier capable of generating voltages and currents at the fundamental frequency expected at the motor terminals is sufficient.

On the other hand, analysing to what extent the inverter controller can suppress torque ripple requires accurate simulation with high-frequency harmonics, which can reach 5 kHz or more, depending on the motor rotation speed and number of poles. Such high-end PHIL motor emulators require a high-bandwidth amplifier controlled by a fast real-time simulator that can create a detailed model. A simulation time around 1 or 2 microseconds and an amplifier with a bandwidth of 5 kHz to 10 kHz will be required to simulate the harmonic current and torque ripples .Starting up the motor also generates short current spikes at the inverter which should be detected by the protection circuit. Testing such high-speed protection is also going to determine the response time and bandwidth required by the amplifier. In practice, to realise real-time high-end motor models, we need a stable amplifier that can handle current spikes and has high bandwidth to simulate harmonic distortion.

**Emulating power grids**

The same analysis should also be performed to implement a distribution and micro grid PHIL simulator. For example, testing a slow micro grid controller with an update time of 50 to 100 milliseconds requires power amplifiers that can generate the nominal grid frequency 50hz to mimic power fluctuations. A simple simulator and an amplifier with not too high bandwidth may suffice. But for simulating very fast overvoltage and overcurrent peaks caused by switching power electronics, we need amplifiers with higher bandwidth controlled in real-time by a fast simulator.

**Selecting a stable and accurate amplifier**

It is also vital to analyse the stability of the closed-loop system formed by the amplifier, the load, the real-time simulator, all sensors and communication links. The aim of this is to obtain a stable PHIL system taking into account all possible delays. Accuracy, stability and overall safe operation of the PHIL system are priorities. In fact, tuning a PHIL system is the same as optimising an operating system where stable running is given absolute priority. Problems must be carefully analysed and all delays caused by the real-time simulator, amplifiers and interface devices must be minimised to increase the accuracy and stability of high-end PHIL systems. Amplifiers with a bandwidth of +/-10 kHz and FPGA-based fast simulators of less than a microsecond are then often required.

The maximum bandwidth of a PHIL application is equal to the maximum frequency capability required to simulate the specified transients and harmonics during the test.

The specifications below are very important to determine the accuracy, speed and stability of the PHIL system.

- Bandwidth determination by bidirectional diagrams showing gain and phase as a function of frequency at different powers and type of loads
- Maximum slew rate and initial delay
- Communication delays to and from the DUT performed by the real-time simulator
- Inductance and impedance
- Sensor accuracy and delay
- Anti-aliasing filters (e.g. if the DUT is an inverter)

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