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

Damping Power System Inter-area Oscillations Through Decoupled Modulation Rui Fan, Shaobu Wang Sept 18 th , 2018 1

Motivation of Decoupled Control 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 Example Small-signal Study Modes couple together When damping mode 1, un-intentionally make mode 2 worse 2

How to decouple (1) Linear system 𝒚(𝑢) = 𝑩𝒚(𝑢) + 𝐶 𝑗 𝑣 𝑗 ) 𝒚(𝑢) = 𝑵𝒜(𝑢 𝒜(𝒖) = 𝑵 −1 𝑩𝑵𝒜(𝒖) + 𝑵 −1 𝑪𝒗 𝒋 = 𝜧𝒜(𝒖) + 𝑶𝑪𝒗𝒋 How to design feedback to 𝜇 1 0 ⋯ 0 ⋯ 0 0 𝜇 2 ⋯ 0 ⋯ 0 move only particular ⋮ ⋮ ⋱ ⋮ ⋱ 0 𝜧 = 𝑵 −1 𝑩𝑵 eigenvalue? 0 0 ⋯ 𝜇 𝑘 ⋯ 0 ⋮ ⋮ ⋱ ⋮ ⋱ 0 0 0 ⋯ 0 ⋯ 𝜇 𝑜 3

How to decouple (2) How to move only one particular eigenvalue? ) 𝒚(𝑢) = 𝑵𝒜(𝑢 𝒜 𝑢 = 𝑵 −1 𝑩𝑵𝒜(𝒖) + 𝑵 −1 𝑪𝒗 𝒋 = 𝜧𝒜 + 𝑶𝑪𝒗 𝒋 𝒍 =[0 0 0 0 … k j … 0 0 0 ] 𝒗 𝒋 = 𝒍𝒜(t) Let , and assume that z i ( t )= c i e λ i t then we have 𝑈 𝐶 𝑗 𝑙 𝑘 𝑛 𝑘 λ 1 0 ⋯ 𝑜 1 ⋯ 0 𝑈 𝐶 𝑗 𝑙 𝑘 𝑛 𝑘 0 λ 2 ⋯ 𝑜 2 ⋯ 0 𝐴 𝑢 = 𝑵 −1 𝑩𝑵𝒜(𝒖) + 𝑵 −1 𝑪𝒗 𝒋 ⋮ ⋮ ⋱ ⋮ ⋱ 0 = 𝜧𝒜(𝒖) + 𝑵 −1 𝑪𝒗 𝒋 A * = 𝑈 𝐶 𝑗 𝑙 𝑘 𝑛 𝑘 0 0 ⋯ λ 𝑘 + 𝑜 𝑘 ⋯ 0 = 𝜧𝒜(𝒖) + 𝑵 −1 𝑪𝒍𝒜 ( t ) ⋮ ⋮ ⋱ ⋮ ⋱ 0 = (𝜧 + 𝑵 −1 𝑪𝒍)𝒜(𝒖) 𝑈 𝐶 𝑗 𝑙 𝑘 𝑛 𝑘 0 0 ⋯ 𝑜 𝑜 ⋯ λ 𝑜 =A * 𝒜 ( t ) Conclusion: if the feedback signal is pure modal signal, then only one corresponding eigenvalue moves. 4

Inspiration of Decouple Control 𝑾(𝒖) = 𝑩 𝟐 𝒇 𝜷 𝟐 𝒖 𝐝𝐩𝐭(𝝏 𝟐 𝒖 + 𝝌 𝟐 ) + 𝑩 𝟑 𝒇 𝜷 𝟑 𝒖 𝐝𝐩𝐭(𝝏 𝟑 𝒖 + 𝝌 𝟑 ) + 𝑩 𝟒 𝒇 𝜷 𝟒 𝒖 𝐝𝐩𝐭(𝝏 𝟒 𝒖 + 𝝌 𝟒 ) + = + 5

Proposed Method Offline study of the system property C Select a chunk of historical oscillation data from n PMUs Apply the Prony’s analysis to determine modal signals 𝑤 𝑗 (𝑢) = 𝐷 𝑗1 𝑛 1 (𝑢) + 𝐷 𝑗2 𝑛 2 (𝑢) + ⋯ + 𝐷 𝑗𝑟 𝑛 1 (𝑢 Determine the matrix C that relates identified modal signals to the given PMU measurements Left-invertible, uniquely determined by system topology and operating point Online mode decomposition Collect measurements from pre- determined n PMUs Determine real-time modal signals based on matrix C 6

PSS Case Study: 2-Area 4-Machine System 2-area 4-machine system 20kV 20kV G1 G3 25km 10km 10km 25km Two major oscillation modes 110km 110km 0.72 Hz 1.15 Hz 20kV 20kV PSS on Generator G4 G2 G4 Target: 1.15 Hz mode Red Dash : true 1.15 Hz Pure Model Blue Solid: Calculated from decouple method 7

PSS Case Study: 2-Area 4-Machine System 2-area 4-machine system 20kV 20kV G1 G3 25km 10km 10km 25km Two major oscillation modes 110km 110km 0.72 Hz 1.15 Hz 20kV 20kV G2 G4 PSS on Generator G4 Target: 1.15 Hz mode Before After 8 8

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 𝛦𝑄 𝑒𝑑 = −𝐿 𝑔 𝑠𝑓𝑑 − 𝑔 𝑗𝑜𝑤 Source: Schoenwald, David A. Wide-Area Damping Control . No. SAND2016-5869PE. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States), 2016. 9

HVDC Case Study: MinniWECC System 10 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 11

HVDC Results 12

HVDC Results Cont. 13

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 14

Questions 15

Backup Slides: Band pass filter When oscillation magnitude differs a lot When difference is small 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 m 2 and the true m 2. 16

Backup Slides: Power System Stabilizer 𝜕 17

Backup Slides: Classical HVDC Damping Control + Pure oscillation 𝛦𝑄 𝑒𝑑 = −𝐿 𝑔 𝑠𝑓𝑑 − 𝑔 + pure_mode(t) modal signal 𝑗𝑜𝑤 Frequency difference is obtained from passing signals of electrical angles difference from PMUs through a derivative filter. 18

Backup Slides: Alberta and BC Modes Alberta Mode BC Mode 19