Sensor Feedback Limitations - Application in a 4-Machine Power System

main_analys.m

This script loads the linearized model by calling the function load_linear_model.m

load_linear_model.m

• Loads a saved linearized model of the Kundur 4-machine 2-area test system.
• Transfer functions used for optimal control design are generated.

Note that the original model contains a lot of obsolete states. Ideally these are removed by taking the minimal realization (matlab function minreal.m). But due to the condition of the model, this generate a significant amount of numerical error, making the control design infeasible. This however, is mainly an issue with the minreal function. To avoid this we instead compute the reduced-order approximation using the built in balred function. This is done in modelred_hsv.m where we have made it easier for the user to select the desired reduced order system size.

If another linearized model is desired (for instance if you want to investigate another load flow scenario) then you will have do some "manual engineering" and revisit the model reduction steps.

Control design

• Synthesize a H2 controller and a PSS-style controller using local phase anlge measurement.
• Compare linear step responses. Note that the real nonlinear simulation will differ quite a bit.
• The choice of PSS gain is obtained by running a root locus. Choose k_pss so that damping of the inter-area mode becomes 10%
• Compare disturbance response ratio between PSS and H2.

Other measurements

Create H2 controllers for

• Complementary external frequency measurement (with time delay)
• Line flow measurement
• Voltage measurement

These are compared with the base line H2 controller using local phase angle measurement, and the uncontrolled system.

Main Simulation

Main file to run nonlinear simulations and plot results

Choices

• Model
• PSS control gain adjustment. Originally tuned down to 20% to give more interesting simulations. Other ways of reducing stability can be to replace the impedance loads with active power loads.
• Load predefined controllers?
• Inertia of generators. Here we consider 75% of the Kundur case just to give more interesting simulations.
• Disturbance step size. (-350 selected)

Run simulations or load from saved file