Damping Power System Inter-area Oscillations Through Decoupled - - PowerPoint PPT Presentation

Damping Power System Inter-area Oscillations Through Decoupled Modulation

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Rui Fan, Shaobu Wang Sept 18th, 2018

Motivation of Decoupled Control

Example

Small-signal Study Modes couple together When damping mode 1, un-intentionally make mode 2 worse

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Inter-area oscillations in power systems

Usually caused by weakly connected tie-lines between areas; Limit the power transfer capacity in tie-line; could lead to large-area blackout

How to decouple (1)

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𝜇1 ⋯ ⋯ 𝜇2 ⋯ ⋯ ⋮ ⋮ ⋱ ⋮ ⋱ ⋯ 𝜇𝑘 ⋯ ⋮ ⋮ ⋱ ⋮ ⋱ ⋯ ⋯ 𝜇𝑜

Linear system How to design feedback to move only particular eigenvalue?

𝜧 = 𝑵−1𝑩𝑵 𝒜(𝒖) = 𝑵−1 𝑩𝑵𝒜(𝒖) + 𝑵−1𝑪𝒗𝒋 𝒚(𝑢) = 𝑩𝒚(𝑢) + 𝐶𝑗𝑣𝑗 ) 𝒚(𝑢) = 𝑵𝒜(𝑢

= 𝜧𝒜(𝒖) + 𝑶𝑪𝒗𝒋

How to decouple (2)

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How to move only one particular eigenvalue?

𝒜 𝑢 = 𝑵−1𝑩𝑵𝒜(𝒖) + 𝑵−1𝑪𝒗𝒋 = 𝜧𝒜 + 𝑶𝑪𝒗𝒋

Let , and assume that then we have

𝒗𝒋 = 𝒍𝒜(t)

𝐴 𝑢 = 𝑵−1𝑩𝑵𝒜(𝒖) + 𝑵−1𝑪𝒗𝒋

= 𝜧𝒜(𝒖) + 𝑵−1𝑪𝒗𝒋

= 𝜧𝒜(𝒖) + 𝑵−1𝑪𝒍𝒜(t) =(𝜧+𝑵−1𝑪𝒍)𝒜(𝒖) =A* 𝒜(t)

A* = λ1 ⋯ 𝑜1

𝑈𝐶𝑗𝑙𝑘𝑛𝑘

⋯ λ2 ⋯ 𝑜2

𝑈𝐶𝑗𝑙𝑘𝑛𝑘

⋯ ⋮ ⋮ ⋱ ⋮ ⋱ ⋯ λ𝑘 + 𝑜𝑘

𝑈𝐶𝑗𝑙𝑘𝑛𝑘

⋯ ⋮ ⋮ ⋱ ⋮ ⋱ ⋯ 𝑜𝑜

𝑈𝐶𝑗𝑙𝑘𝑛𝑘

⋯ λ𝑜 𝒍=[0 0 0 0 … kj… 0 0 0 ]

Conclusion: if the feedback signal is pure modal signal, then only one corresponding eigenvalue moves.

) 𝒚(𝑢) = 𝑵𝒜(𝑢 zi (t)= ci eλi t

Inspiration of Decouple Control

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=

+ +

) 𝑾(𝒖) = 𝑩𝟐𝒇𝜷𝟐𝒖𝐝𝐩𝐭(𝝏𝟐𝒖 + 𝝌𝟐) + 𝑩𝟑𝒇𝜷𝟑𝒖𝐝𝐩𝐭(𝝏𝟑𝒖 + 𝝌𝟑) + 𝑩𝟒𝒇𝜷𝟒𝒖𝐝𝐩𝐭(𝝏𝟒𝒖 + 𝝌𝟒

Proposed Method

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Offline study of the system property

Select a chunk of historical oscillation data from n PMUs Apply the Prony’s analysis to determine modal signals Determine the matrix C that relates identified modal signals to the given PMU measurements Left-invertible, uniquely determined by system topology and operating point 𝑤𝑗(𝑢) = 𝐷𝑗1𝑛1(𝑢) + 𝐷𝑗2𝑛2(𝑢) + ⋯ + 𝐷𝑗𝑟𝑛1(𝑢

Online mode decomposition

Collect measurements from pre- determined n PMUs Determine real-time modal signals based

• n matrix C

C

PSS Case Study: 2-Area 4-Machine System

2-area 4-machine system Two major oscillation modes

0.72 Hz 1.15 Hz

PSS on Generator G4 Target: 1.15 Hz mode

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20kV

G1

20kV

G2

20kV

G4

20kV

G3

25km

10km 110km 110km

10km

25km

Red Dash : true 1.15 Hz Pure Model Blue Solid: Calculated from decouple method

PSS Case Study: 2-Area 4-Machine System

2-area 4-machine system Two major oscillation modes

0.72 Hz 1.15 Hz

PSS on Generator G4 Target: 1.15 Hz mode

8

20kV

G1

20kV

G2

20kV

G4

20kV

G3

25km

10km 110km 110km

10km

25km

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Before After

Use HVDC to Damp Inter-Area Oscillations

HVDC transmission is expanding, it controls the power transfer between different areas SNL has installed a damping controller on the PDCI of WECC system

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Source: Schoenwald, David A. Wide-Area Damping Control. No. SAND2016-5869PE. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States), 2016.

𝛦𝑄𝑒𝑑 = −𝐿 𝑔

𝑠𝑓𝑑 − 𝑔 𝑗𝑜𝑤

HVDC Case Study: MinniWECC System

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Source: MinniWECC system by Dr. Trudnowski

Using PDCI to Damp Oscillations

Pacific DC Intertie (PDCI or Path 65)

From Celilo converter station at Dalles, Oregon, to the Sylmar converter station north of Los Angeles ±500 kV DC, 2,850 MW Capacity 846-mile route

Event: At time 1.0 sec, a small pulse perturbation is added to the machine 10 to trigger the inter-area oscillations Target Mode: BC mode (0.632 Hz, 1.0%) Three cases are studied

No control Classical control Classical control + decoupled control

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HVDC Results

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HVDC Results Cont.

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Summary

Classical HVDC damping control is effective on damping inter- area oscillations, while it usually damps ALL oscillation modes Decouple Modulation can work along with the classical method to further increase the damping of concerned oscillation mode precisely Decouple modulation using other devices except HVDC or PSS:

Load modulation FACTS Generator Output Power Control (via Governor)

More research is required on matrix C

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Questions

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Backup Slides: Band pass filter

the performance of the band-pass filter depends on the difference of input signals. The filter works well when the target mode is high; however the performance degrades fast as the proportion decreases. There is a phase shift between the extracted m2 and the true m2.

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When oscillation magnitude differs a lot When difference is small

Backup Slides: Power System Stabilizer

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𝜕

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Backup Slides: Classical HVDC Damping Control

𝛦𝑄𝑒𝑑 = −𝐿 𝑔

𝑠𝑓𝑑 − 𝑔 𝑗𝑜𝑤

Frequency difference is obtained from passing signals of electrical angles difference from PMUs through a derivative filter.

+

Pure oscillation modal signal

+ pure_mode(t)

Backup Slides: Alberta and BC Modes

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Alberta Mode BC Mode