Wide-Area Modeling, Analysis and Control of Large-Scale Power - PowerPoint PPT Presentation

Wide-Area Modeling, Analysis and Control of Large-Scale Power Systems using Synchrophasors Aranya Chakrabortty North Carolina State University, Raleigh, NC Information Trust Institute at UIUC 7 th October, 2011

Wide Area Measurements (WAMS) • 2003 blackout in the Eastern Interconnection EIPP (Eastern Interconnection Phasor Project) NASPI (North American Synchrophasor Initiative) Power System Research Consortium (PSRC, 2006-present) Industry Members • Rensselaer (Joe Chow, Murat Arcak) • Virginia Tech (Yilu Liu) • Univ. of Wyoming (John Pierre) • Montana Tech (Dan Trudnowski) • Technical Research (RPI) 1. Model Identification of large-scale power systems 2. Post-disturbance data Analysis 3. Controller and observer designs, robustness, optimization 2

Main trigger: 2003 Northeast Blackout NYC before blackout New England Ohio Power flow INTER-AREA INTER-AREA STABLE UNSTABLE NYC after blackout Hauer, Zhou & Trudnowsky, 2004 Kosterev & Martins, 2004 Lesson learnt: 1. Wide-Area Dynamic Monitoring is important 2. Clustering and aggregation is imperative 3

Main trigger: 2003 Northeast Blackout NYC before blackout New England Ohio Power flow INTER-AREA INTER-AREA STABLE UNSTABLE NYC after blackout Hauer, Zhou & Trudnowsky, 2004 Kosterev & Martins, 2004 Lesson learnt: 1. Wide-Area Dynamic Monitoring is important 2. Clustering and aggregation is imperative 3

Model Aggregation using distributed PMU data 6-machine, 30 bus, 3 areas Problem Formulation: 1. Model Reduction • How to form an aggregate model from the large system PMU PMU PMU • Chakrabortty & Chow (2008, 2009, 2010), Chakrabortty & Salazar (2009, 2010) 4

Model Aggregation using distributed PMU data 6-machine, 30 bus, 3 areas Problem Formulation: 1. Model Reduction • How to form an aggregate model from the large system PMU Area 1 PMU PMU Aggregate Transmission Network Area 3 Area 2 • Chakrabortty & Chow (2008, 2009, 2010), Chakrabortty & Salazar (2009, 2010) 4

One-Dimensional Models ~    I I I PMU PMU   1   E E 2 2 1 H 1 H 2 ~ ~  V    V   x 2 x 1 x e V V 1 1 1 2 2 2 5

One-Dimensional Models ~    I I I PMU PMU   1   E E 2 2 1 H 1 H 2 ~ ~  V    V   x 2 x 1 x e V V 1 1 1 2 2 2     Problem:  How to estimate all parameters? H H H P H P E E     1 2  2 1 1 2 1 2 m m 2 sin     ( H H H H x x x 1 2 ) e 1 2 1 2 x 1 , x 2 , H 1 , H 2 Swing Equation 5

IME: Method ( Reactance Extrapolation) • Key idea : Amplitude of voltage oscillation at any point is a function of its electrical distance from the two fixed voltage sources. 2  1   2 0 E E 1 ~ ~ ~ I V V 1 2 x 1. Choose a measured variable: Say, voltage magnitude 6

IME: Method ( Reactance Extrapolation) • Key idea : Amplitude of voltage oscillation at any point is a function of its electrical distance from the two fixed voltage sources. 2  1   2 0 E E 1 ~ ~ ~ I V V 1 2 x ~ x        ( ) [ ( 1 ) cos( ) ] sin( ), V x E a E a j E a a  e  2 1 1 x x x 1 2 ~         2 2 2 2 2 • Voltage magnitude : | ( ) | 2 ( ) cos( ) , ( 1 ) V V x c E E a a c a E a E 2 1 1 2 6

IME: Method ( Reactance Extrapolation) • Key idea : Amplitude of voltage oscillation at any point is a function of its electrical distance from the two fixed voltage sources. 2  1   2 0 E E 1 ~ ~ ~ I V V 1 2 x ~ x        ( ) [ ( 1 ) cos( ) ] sin( ), V x E a E a j E a a  e  2 1 1 x x x 1 2 ~         2 2 2 2 2 • Voltage magnitude : | ( ) | 2 ( ) cos( ) , ( 1 ) V V x c E E a a c a E a E 2 1 1 2 • Assume the system is initially in an equilibrium ( δ 0 , ω 0 = 0, V ss ) :      ( ) ( , ) V x J a 0    ( , ) V a E E      2 0 1 2 ( , ) : ( ) sin( ) J a a a 0    0 ( , ) V a    0 0 6

Reactance Extrapolation         2 ( , ) ( , ) sin( ) ( ) ( t ) V x t V a E E a a 0 1 2 0 can be computed A from measurements at x 7

Reactance Extrapolation         2 ( , ) ( , ) sin( ) ( ) ( t ) V x t V a E E a a 0 1 2 0 can be computed A from measurements at x     2 ( , ) ( ) ( t ) V n x t A a a Note: Spatial and temporal dependence are separated 7

Reactance Extrapolation         2 ( , ) ( , ) sin( ) ( ) ( t ) V x t V a E E a a 0 1 2 0 can be computed A from measurements at x     2 ( , ) ( ) ( t ) V n x t A a a Note: Spatial and temporal dependence are separated     2 ( , *) ( ) ( *) V n x t A a a t • Fix time: t=t* How can we use this relation to solve our problem? 7

Reactance Extrapolation     2 ( , *) ( ) ( *) V n x t A a a t PMU PMU 2  1   2 0 E E 1 8

Reactance Extrapolation     2 ( , *) ( ) ( *) V n x t A a a t PMU PMU 2  1   2 0 E E 1 x 2 x 2      2 ( ) ( *) At Bus 2, a V A a a t 2 , 2 2 2 n Bus  e  x x x 1 2 8

Reactance Extrapolation     2 ( , *) ( ) ( *) V n x t A a a t PMU PMU 2  1   2 0 E E 1 x 2 x e + x 2 x 2      2 ( ) ( *) At Bus 2, a V A a a t 2 , 2 2 2 n Bus  e   x x x 1 2 ( 1 ) V a a n , Bus 2 2 2    x x ( 1 ) V a a e 2      , 1 1 1 2 n Bus At Bus 1, a ( ) ( *) V A a a t 1   , 1 1 1 n Bus x x x 1 e 2 • Need one more equation - hence, need one more measurement at a known distance 8

Reactance Extrapolation     2 ( , *) ( ) ( *) V n x t A a a t 3 PMU PMU 2  1   2 0 E E 1 PMU x 2 x x  e 2 2 x e + x 2 x 2      2 ( ) ( *) At Bus 2, a V A a a t 2 , 2 2 2 n Bus  e   x x x 1 2 ( 1 ) V a a n , Bus 2 2 2    x x ( 1 ) V a a e 2      , 1 1 1 2 n Bus At Bus 1, a ( ) ( *) V A a a t 1   , 1 1 1 n Bus x x x 1 e 2  • Need one more equation ( 1 ) V a a , 3 3 3 n Bus  - hence, need one more measurement at a known distance  ( 1 ) V a a n , Bus 1 1 1 8

Reactance Extrapolation V n ( a ) = A a (1 - a ) V 3n V 2n V 1n x e / 2 x e / 2 x 2 x 1 Key idea: Exploit the spatial variation of phasor outputs 9

IME: Method ( Inertia Estimation) • From linearized model   1 cos( ) E E  1 2 0 f    s 2 2 ( ) H x x x e 1 2 H H  where f s is the measured swing frequency and 1 2 H  H H 1 2 • For a second equation in H 1 and H 2 , use law of conservation of angular momentum                 2 2 2 ( ) ( ) 0 H H H H dt P P P P dt 1 1 2 2 1 1 2 2 1 1 2 2 m e m e  • Reminiscent of Zaborsky’s result H   1 2   H H   1 2 2 1  H 2 1 • However, ω 1 and ω 2 are not available from PMU data, Estimate ω 1 and ω 2 from the measured frequencies ξ 1 and ξ 2 at Buses 1 and 2 10

IME: Method ( Inertia Estimation) • Express voltage angle θ as a function of δ , and differentiate wrt time to obtain a relation between the machine speeds and bus frequencies: where,           ( ) cos( ) a b c   1 1 1 1 2 1 2 1 2 1          2 cos( ) 2 2 a b c ( 1 ) , ( 1 ), a E r b E E r r 1 1 1 2 1 1 1 2 i i i i i  2 2 c E r           ( ) cos( ) a b c 2 i i   2 1 2 1 2 1 2 2 2      2 2 cos( ) a b c 0.6 2 2 1 2 2 0.4 • ξ 1 and ξ 2 are measured, and a i , b i , c i Frequency (r/s) are known from reactance extrapolation. 0.2 x e x 1 x 2 • Hence, we calculate ω 1 / ω 2 to solve 0 for H 1 and H 2 . -0.2 -0.4 0 0.2 0.4 0.6 0.8 1 Normalized Reactance r 11

Illustration: 2-Machine Example • Illustrate IME on classical 2-machine model ( r e = 0) • Disturbance is applied to the system and the response simulated in MATLAB    0 . 0292 0 . 0316 0 . 0371 V V V 1 2 3 m m m    1 . 0320 1 . 0317 1 . 0136 V V V 1 ss 2 ss 3 ss    0 . 0301 0 . 0326 0 . 0376 V V V 1 2 3 n n n IME Algorithm Exact values: x 1 = 0.3382 pu x 1 = 0.34 pu, Voltage oscillations at 3 buses x 2 = 0.3880 pu x 2 = 0.39 pu s H 1 = 6.48 pu  sT IME ( ) G s  H 2 = 9.49 pu 1 Exact values: H 1 = 6.5 pu, H 2 = 9.5 pu Bus angle oscillations Bus frequency oscillations 12