This example shows how to perform frequency scans to obtain Single-Input Single-Output Transfer Functions (TF). Power systems entail a high degree of complexity and analytically representing their dynamics by transfer functions can be very challenging. Nonetheless, knowing the frequency response of a process provides very valuable information to better understand different phenomena involved as well as to mitigate certain problems and/or design better controllers. Therefore, the function frequency_sweep_TF automatically extracts the transfer function between any given quantities in an EMT model.
In order to be as general as possible, the model for this example is very simple so the results can also be verified analytically. Yet, the functionalities also apply to more complex non-linear systems; for example, the modulation TF of the MMC is examined in this paper.
It is assumed that the pre-requistes are installed. Similarly to the other examples, when opening the TF_test.pswx PSCAD workspace in this folder, the Z-tool library will appear grayed-out as it points to the computer where it was last saved. Therefore, in the PSCAD project simply unload the grayed-out library by right-cliking on it and selecting Unload, then add the library file Z_tool.pslx within the Z-tool installation path in your PC (Scan folder at the directory retrieved by cmd py -m pip show ztoolacdc), move it up before your project files and save the changes.
As shown below, the model contains two identical closed-loop systems comprised of a PI controller acting on a plant including a second-order transfer function and a time delay. Two TF scan blocks are used to extract the different dynamics of the system:
- CL: inserted in the reference path, i.e at the input of the controller, and the output is measured. This configuration is used to obtain the reference-to-output closed-loop response.
- OL: placed between the output of the controller and the plant's input while measuring the output; this setup is used to obtain the control action-to-output open-loop response.
The TF scan block working principle is similar to the AC and DC scan blocks as it continously feeds its left-side input through (no action) until the decoupling time defined in the frequency_sweep_TF argument t_snap is reached. Then the block supperimposes sinusoidal perturbations on top of the held input so as to generate the new input or excitation signal on its right-side to be fed to the system under study. This signal represents the input of the target transfer function to be scanned. The output pin can be connected to any signal of interest and it represents the output of the transfer function of interest.
Once the model is setup, the scan parameters need to be provided in the corresponding python script TF_example.py. The frequency_sweep_TF function accepts similar arguments as the frequency_sweep function already used in the other examples, such as num_parallel_sim and multi_freq_scan. However, instead of specifying the electical topology this function accepts the target_blocks argument, which is a list of strings corresponding to the target TF scan block names in the model. This argument specifies which TFs are scanned, and those not specified are simply ignored. If target_blocks is not provided, then all TF scan blocks are scanned. For example, target_blocks=["CL"] would only scan the TF corresponding to the CL TF scan block without affecting the other OL TF scan block.
Since the particular system under study is linear time invariant (LTI), its dynamics do not change depending on its inputs, states or when these are altered. Therefore, the snapshot time can be set arbitrarily and no subsequent waiting time is needed, i.e. dt_injections=0. Note that this only applies to LTI systems. To illustrate the null impact of the unsteady dynamics prior to the perturbations, the plot_snapshot argument is set to True so as to generate both time and frequency-domain plots of the snapshot waveforms during the simulation startup. In addition, by setting plot_perturbation=1 plots corresponding to the first perturbation are produced, as shown below.
For more information on the function arguments, open a python shell, import the function e.g. from ztoolacdc.frequency_sweep import frequency_sweep_TF, and type help(frequency_sweep_TF).
The progress is reported during the execution, and the results can be accessed in the especified results_folder. As shown below, the scanned TF (black dots) very well matches the expected TF (green).
Note that the frequency_sweep_TF function only works with TF scan blocks, while frequency_sweep only works with AC scan and DC scan blocks. In addition, frequency_sweep_TF currently only supports SISO scans, while frequency_sweep allows for MIMO scans of any size and between any analysis points. Note that you can retrieve single-input multiple-output transfer functions by using a main scan block to excite the system (single input) and other dummy scan blocks to measure the multiple outputs of interest. Ongoing work includes the improvement of frequency_sweep_TF to also retrieve MIMO TFs.