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Example | Kundur 4-Machine Power System


This example model can be found in the software under the category "Benchmarks" with the file name "Kundur_4Machines.ecf".


The 4-machines Kundur model is developed in HYPERSIM based on the Kundur book example on page 813 [1]. The model consists of two symmetrical areas linked together by two 230 kV lines of 220 km length. It was specifically designed to study low-frequency electromechanical oscillations in large-interconnected power systems. The model was modified from the original example by adding 187 Mvar of additional capacitance in each power system area to have a unity load voltage profile, similarly to how the Simscape example model is setup [2].

Each area is equipped with two identical round rotor synchronous machines rated 20 kV/900 MVA. Each machine is controlled by an exciter SCRX, governor TGOV1, and two options of power system stabilizers PSS1A or PSS4B. SM2 in the first area is the slack machine, whereas the rest of the machines are PV machines. Each of the machines generates around 700 MW of power. The loads are constant impedances and are split between the areas in such a way that area 1 is exporting 413MW to area 2. The reference load-flow with M2 considered the slack machine is such that all generators are producing about 700 MW each. The machine controllers are tuned such that the model is stable in steady-state.

The user has three choices for the use of a power system stabilizer, summarized in the table below. The choice can be made by changing the value of the constant “To_select_PSS” which can be found in the bottom left of the schematic page. The default value of this constant in the model is 2.

Constant value



No power system stabilizer





Below is a figure of the subsystem contents showing the synchronous machine and its controllers.

The following table contains the model load flow results at the machines.

Machine name


Voltage (pu)

Angle (deg)

P (MW)


























Simulation and Results

Scenario 1: EFD Perturbation

As part of the setup of the example mode, the user can conduct two types of scenarios. The first scenario is about introducing a perturbation to the exciter output feeding the Efd_i input of the synchronous machine at a selected machine. This scenario gives the user a simplified way to study and improve the tuning of the involved machine controllers in the system. The perturbation is an applied gain of 1.1 for 0.5 seconds after 5 seconds of acquisition. The user can change these settings by going into the machine subsystem and changing the values of Gain1 and the DelayOn1. To choose which machine to apply the perturbation to, the choice can be made by changing the value of the constant “Perturb_selection” that can be found in the bottom left corner of the schematic page. Below is a table listing the available options. The default value of this constant in the model is 1.

Constant value



No perturbation anywhere


Perturb EFD of SM1


Perturb EFD of SM2


Perturb EFD of SM3


Perturb EFD of SM4

The following are the results from ScopeView following a perturbation at SM1.

The following figure shows the difference in the response of the SM1 terminal voltage when using either of the three stabilizer options. As can be noticed, with PSS4B, the machine terminal voltage have the best settling time. On the other hand, the PSS1A has the least overshoot but has the largest settling time. It is clear that the PSS1A could use further tuning to improve the response of the system but it is left as an exercise for the HYPERSIM user.

Scenario 2: Short Circuit Test

To demonstrate the response of the system in a real-life scenario, the model is equipped with a short-circuit test and can be activated by checking the trigger option in the ScopeView template associated with the model. By default, the ScopeView template does not have the Trig checked. The following is a snapshot of ScopeView settings:

The default short-circuit scenario is a 3-phase-ground fault of 1e-3 ohms applied at t = 5 s at bus 9 located in the middle of the intersection, followed by tripping Dline1 and Dline2 by opening breakers BR1 and BR2 at t = 5.1 s. At t = 25 s, the line circuit breakers close again to allow the user to rerun the fault scenario. 

Prior to running this scenario, the user should not forget to set the Perturb_selection value to zero in order not to apply the first scenario. The following are the results.

The following figure shows the difference in the response of the SM1 terminal voltage when using either of the three stabilizer options. As can be noticed, without a power system stabilizer, the power system goes unstable. With PSS1A, the power system remains stable but undergoes large voltage oscillations. Finally with PSS4B, the system maintains voltage stability and reaches steady-state with a good settling time.


[1] P. Kundur, Power system stability, and control, vol. 7. McGraw-hill New York, 1994, Example 12.6, p. 813.

[2] I. Kamwa, Performance of Three PSS for Interarea Oscillations, SimPowerSystems Demo, Hydro-Québec.

See Also

Synchronous Machine (pu Standard)TGOV1SCRXPSS1APSS4B

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