Masters of Engineering Small Signal Stability Aaron Cowan Electrical Engineering Power

Small Signal Stability Exciter Field current Terminal voltage Power System Stabilizer Enhance stability Rotor angle Equal Area Criterion (Fig 13.5, Kundur) Aa < Ad Aa > Ad

SMIB Example Problem details in section 12.3 of Power System Stability and Control, Kundur

Results Kundur ωd = 1.05Hz ξ = 0.15 KS = 0.829 KD = 14.08 Matlab ξ = 0.1447 KS = 1.1062 KD = 15.6306 State Matrix and eigenvalues agree 0 −0.109 −0.123 0 0 0 376.99 0 0 0 0 0 0 −0.193 −0.4229 −27.317 0 27.317 0 −7.312 20.839 −50 0 0 0 −1.037 −1.173 0 −0.714 0 0 −4.840 −5.477 0 26.969 −30.303 Δ𝜔𝑟 Δ𝛿 Δ𝜓𝑓𝑑 Δ𝜈1 Δ𝜈2 Δ𝜈𝑠 A = 𝜆2=0.504+𝑗7.23 ←𝑒𝑖𝑔𝑒𝑛𝑣𝑎𝑙𝑢𝑒 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑟𝑜𝑡𝑜𝑟 𝑎𝑛𝑔𝑙𝑒

Power World Transient Stability WECC equivalent in Power World

Exciter Models

Exciter Models

Exciter Models

PSS Model

IEEE 421.2

SMIB – Power World { Equivalent SMIB State Matrix Eigenvalues

Power World Transient Stability WECC equivalent in Power World

Stability Simulation Default values used Did change TR to 0.02 in all cases SEXS_GE and STAB1 ↔ Fig 17.5, Kundur Set all generator stability models equal Innumerable permutations

Stability Simulation Fault on line 7-5 Three cases for each Exciter Both breakers open Cleared in 0.07 sec Three cases for each Exciter Each generator Three cases for each Exciter+PSS

Generator 1

Generator 1: ESAC1A 𝑀𝑊0=71.6 𝛿0=3.5° 𝑀𝑊𝑐𝑙𝑒𝑎𝑟=70.6 𝛿𝑐𝑙𝑒𝑎𝑟=−5.3°

Generator 2

Generator 2: ESDC1A 𝑀𝑊0=163 𝛿0=61.1° 𝑀𝑊𝑐𝑙𝑒𝑎𝑟=163 𝛿𝑐𝑙𝑒𝑎𝑟=70.7°

Generator 3

Generator 3: SEXS_GE 𝑀𝑊0=85 𝛿0=54.1° 𝑀𝑊𝑐𝑙𝑒𝑎𝑟=85 𝛿𝑐𝑙𝑒𝑎𝑟=51.9°

Summary Power World Transient Stability ESDC1A without PSS Block Diagrams SMIB Eigenvalues ESDC1A without PSS SEXS_GE with PSS PSS stability enhancement

Small Signal Stability Questions?

Generator 1: ESDC1A

Generator 1: SEXS_GE

Generator 2: ESAC1A

Generator 2: SEXS_GE

Generator 3: ESDC1A

Generator 3: ESAC1A