Investigating Extreme Oscillations in Low-Inertia Generators within IEEE 39-Bus System with Heterogeneous Inertia Constants

[Barbara258]

Dear Hantao Cui,

I've encountered an interesting phenomenon while simulating load disturbances in the IEEE 39-bus system with different generator inertia settings. I'm seeking your insights on the following behavior:

When generators have significantly different inertia constants (M values), and I apply a sudden load increase disturbance to the system, I observe extreme oscillations in both rotor speed and COI frequency specifically for the low-inertia generators (as shown in Figures 1 ). The oscillations appear highly erratic and significantly differ from the expected frequency response pattern.

However, when I set the generator inertia constants to be more homogeneous (with smaller differences between units), these extreme oscillations disappear, and all generators show more consistent frequency responses (as shown in Figures 2).

My specific settings in the heterogeneous case were:

• COI 1: M values of 25-30 (ultra-high inertia)
• COI 2: M values of 10-12 (medium inertia)
• COI 3: M values of 3-4 (low inertia)
• COI 4: M values of 2 or lower (extremely low inertia)

While in the homogeneous case, all generators had M values between 6-15.

What causes these extreme oscillations specifically in low-inertia areas under heterogeneous conditions? Is this related to numerical instability in the simulation, or does it represent actual physical phenomena we might observe in real power systems with high penetration of inverter-based resources?

Any insights on the underlying mechanisms and potential mitigation strategies would be greatly appreciated.

Thank you

[cuihantao]

For a system with generators of low inertia, you will expect to see large rate of change of frequency at these generators. This is not numerical instability - the result appears stable. It's possibly just due to the fact that some generator inertia is low. You can gradually increase them to see the smooth out of the curves, or you can do an eigenvalue analysis of the steady-state system, which should show the same oscillation frequency that is observed.

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On Mar 25, 2025, at 2:38 AM, Barbara258 ***@***.***> wrote: <x-msg://8/url>Dear Hantao Cui, I've encountered an interesting phenomenon while simulating load disturbances in the IEEE 39-bus system with different generator inertia settings. I'm seeking your insights on the following behavior: When generators have significantly different inertia constants (M values), and I apply a sudden load increase disturbance to the system, I observe extreme oscillations in both rotor speed and COI frequency specifically for the low-inertia generators (as shown in Figures 1 ). The oscillations appear highly erratic and significantly differ from the expected frequency response pattern. However, when I set the generator inertia constants to be more homogeneous (with smaller differences between units), these extreme oscillations disappear, and all generators show more consistent frequency responses (as shown in Figures 2). My specific settings in the heterogeneous case were: COI 1: M values of 25-30 (ultra-high inertia) COI 2: M values of 10-12 (medium inertia) COI 3: M values of 3-4 (low inertia) COI 4: M values of 2 or lower (extremely low inertia) While in the homogeneous case, all generators had M values between 6-15. What causes these extreme oscillations specifically in low-inertia areas under heterogeneous conditions? Is this related to numerical instability in the simulation, or does it represent actual physical phenomena we might observe in real power systems with high penetration of inverter-based resources? Any insights on the underlying mechanisms and potential mitigation strategies would be greatly appreciated. Thank you 1.png (view on web) <https://github.com/user-attachments/assets/d0f66b34-69da-47c7-b058-eddfca409b72> 2.png (view on web) <https://github.com/user-attachments/assets/33b2f60c-83d5-4ff7-98aa-e4a73ca20fbe> — Reply to this email directly, view it on GitHub <#594>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABSNZA6QVKK3F6GXWXBOO3D2WD2UXAVCNFSM6AAAAABZWXZF66VHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZYGEZDKNZWHA>. You are receiving this because you are subscribed to this thread.

[Barbara258]

Thank you for your response. Regarding your explanation about low inertia causing frequency rate of change oscillations, I still have some questions.

I'm using the built-in ieee39_full.xlsx model in ANDES for my simulations, only modifying the inertia constants and adding COI models, with COI area divisions as shown in Figure 1.

I've noticed that even when I set generator inertias quite low (the time constants M for all 10 generators set to: 6,5,4,6,5,4,6,5,4,6), as long as the inertia constants don't vary significantly between generators, the COI frequency curves for different areas remain smooth, as shown in Figure 2. In this case, why don't we see oscillations despite the low inertia and higher rate of frequency change?

However, when I set one generator with much higher inertia (generator inertia constants: 6,5,4,6,5,4,6,5,4,80), the COI frequencies in different areas exhibit oscillations as highlighted in the red box in Figure 3. What causes this phenomenon? Is it related to inter-area oscillation modes?

Additionally, as shown in Figure 3, I've found that the frequency nadirs across different areas don't differ significantly (only about 0.01Hz), even with large differences in their inertia values. What causes this small difference? Is it related to the strength of tie-line power transfers? Which parameters could be adjusted to observe more pronounced differences?

[cuihantao]

You can do a small-signal stability analysis on the heterogeneous inertia case and see the oscillation modes.

The result is somewhat expected because if you imagine a spring network with both heavy and light springs, the light springs will oscillate faster and may oscillate against each other, while the heavier ones will respond slower.