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电子图书
电子图书名:
Power System Modelling and Scripting
编者:
Federico Milano
内容简介:
"Power system modelling and scripting" is a quite general and ambitious title. Of course, to embrace all existing aspects of power system modelling would lead to an encyclopedia and would be likely an impossible task. Thus, this book focuses on a subset of power system models based on the following assumptions: devices are modelled as a set of nonlinear differential algebraic equations; all alternate-current devices are operating in three-phase balanced fundamental frequency, and the time frame of the dynamics of interest ranges from tenths to tens of seconds. These assumptions basically restrict the analysis to transient stability phenomena and generator controls. The modelling step is not self-sufficient. Mathematical models have to be translated into computer programming code in order to be analyzed, understood and 'experienced'. It is an object of this book to provide a general framework for a power system analysis software tool and hints for filling up this framework with versatile programming code. This book is for all students and researchers that are looking for a quick reference on power system models or need some guidelines for starting the challenging adventure of writing their own code.
所属专业方向:
电力系统及其自动化
出版社:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K (2010年8月1日)
来源:
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Contents0 K9 i" ^2 R1 c* S ! N9 X. F7 Y6 B& u5 K3 j- q$ ? ! }5 K) t! U) S3 _ - l( s: V5 q2 p5 n; D7 [; a6 a 1.2 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4# o0 I, h" B) B' t 1.3 Modelling Physical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. O! b4 D2 w# S# K 8 B+ p( y8 I7 w- j3 o" [7 T& S 6 V- r9 [" O, ^ * v/ |& x2 g7 S E4 O 3 `, V! V- n- A, m Z4 v. h X% g$ Q% m! D- p, ]$ X) W9 \2 M ) a' s _# [5 O' X* g + X8 ~. B/ K2 _7 ?: c 3.1 Open and Closed Programming . . . . . . . . . . . . . . . . . . . . . . . . . 31; f' ~: V4 N& a5 w' W' v! r: M 3.2 Scripting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 \" w6 e! q: y6 R: Z0 N+ N# i" m 3.3 Scripting Languages for Computational Science . . . . . . . . . . . 35- U/ V: m1 Q) j 5 O- @3 _/ @# v+ J 3.5 Python Scripting Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39" D9 R7 o3 q* w+ s- h9 A% O $ m& U6 k, L+ y# \- o: f 4 Power Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 J8 ]" ]9 H; a; [ 4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61/ j H" ^- [; O* x0 j+ v 4.2 Taxonomy of Power Flow Problems . . . . . . . . . . . . . . . . . . . . . . 66: x) h( U3 L7 |8 i2 a! \ " {9 t* K! e) I 7 a1 P* Z% {3 i% ` 4.4.1 Jacobi and Gauss-Seidel’s Method. . . . . . . . . . . . . . . . 70 V% { W) Q+ H5 i+ V, v 4.4.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74% x; H3 e% Q9 ?& { C ' }7 O" E; m. W! }* n! {. K: ~! V' Z 4.4.3 Power Flow Jacobian Matrix . . . . . . . . . . . . . . . . . . . . 77( z/ n' x4 A5 w1 |6 m4 _4 J 4.4.4 Robust Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . 82% P8 E# H' n1 }2 q9 V & \; Q5 R. e$ M9 t * @( v3 Q7 N& E s* x/ g& |& v+ }+ O $ G1 p$ f: B0 S2 i m! R+ D 4.4.8 DC Power Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 929 x2 c* L( Z N: n+ r 4.4.9 Single and Distributed Slack Bus Models . . . . . . . . . . 95$ n( ?/ v% ?+ j% z . V0 C" S1 L0 e, N. O: j 4.5.1 Stability of the Continuous Newton’s Method . . . . . . 97) X- ~0 x! B4 |: f `' r! f. A" G 4.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001 h$ v: p1 V- W |# V " q6 a- \5 ?+ F' C 5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1039 |, q) Z& x/ p4 K2 h7 R . _& J; B7 _, q( [" k5 N$ [ 2 X$ I7 A# e1 n7 K; k' W9 O 5.3.1 Saddle-Node Bifurcation . . . . . . . . . . . . . . . . . . . . . . . . 1099 X* ^7 @2 D: I" c0 {3 K2 K 5.3.2 Limit-Induced Bifurcation. . . . . . . . . . . . . . . . . . . . . . . 111 T j7 y- M' ] 5.3.3 Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . 1137 z6 D5 {+ o" j* J; V! L 5.4 Homotopy Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114" b/ U$ A- Q6 `+ `, T 6 b% F+ e5 h" A* I $ Q5 w5 g* i, ]0 C! r# A 5.4.3 Corrector Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121; v$ _' i/ q9 Y& e9 ]7 `7 N 5.4.4 Continuous Newton’s Method and Homotopy . . . . . . 1268 f+ X2 \- ?/ N1 p3 F" e8 p 5.4.5 N-1 Contingency Analysis . . . . . . . . . . . . . . . . . . . . . . . 127& [: ?, K' z" P0 F/ O/ R ( C: d! X& e( j2 B! t* O4 H 6 Optimal Power Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131, ]3 V* E3 Q0 I/ c% K* L 8 @% _' H# C5 n& A, v- L) G( p 6.2 Optimal Power Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337 x. D9 x( Q @ 6.3 Nonlinear Programming Solvers . . . . . . . . . . . . . . . . . . . . . . . . . 1394 V8 B' u! W H! ^) S 6.3.1 Generalized Reduced Gradient Method . . . . . . . . . . . 1409 G) s2 o3 ?# c4 P! h8 T/ E 6.3.2 Interior Point Method . . . . . . . . . . . . . . . . . . . . . . . . . . 142/ k' D5 J+ R. X/ _& T 4 G1 A, q _' D5 g2 W / x7 e0 I: _ r, q) G # a4 s, A; ?2 s 5 b# S3 F0 k, C 7.2.1 Bifurcation Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161& u/ b) i2 r J7 ^ 7.2.2 Participation Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 165, L5 n. p, J" r' y! s2 d F 7.2.3 Analysis in the Z-Domain. . . . . . . . . . . . . . . . . . . . . . . 1697 Z* }# ?% e5 Z& D9 Q 0 H/ C; [ F1 C8 q& `8 A9 G: S 6 v T& O2 I, n' e3 \$ G & n. b. J2 N: E ! g; ?4 s X; R$ W' q1 H' Q0 K * _) z8 X# @8 d! r& R7 U. \8 E " j' r( v9 N& c8 ~ 7.4.1 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . 174) f l7 y( X0 Z7 O. a9 z4 T" I 0 I! L7 _6 K6 W9 s: g 8 Time Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1790 Z- m" C+ t$ t. q 8.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1794 m& {0 }: x" n4 Q- S# [ 9 i9 n9 t" \1 W % `; A/ i7 K6 Z' r9 f7 G 8.2.2 Power-Injection Model . . . . . . . . . . . . . . . . . . . . . . . . . . 189/ Y4 _$ y- A* Y + e4 K) q' I% T0 F7 z 8.3.1 Explicit Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1921 h- V+ z- i% c; J1 ? # o4 j! A6 r+ C7 s) L: L( O. J b ' E% ]$ x7 n6 c, B* X, }+ q5 A h 8.4.1 Step Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2000 S) n! Q" O; V, ]/ n - _6 G1 P* E M1 X) d/ | 8.4.3 Stop Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204: \3 ^ Y% F7 x8 f h , ^1 n$ |6 R* J3 D3 G 8.6 Quasi-static Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2136 ?8 n, x5 k! h1 a# g2 `2 s 8.7 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2173 ^" i8 b; p3 r$ Y: q0 l( \ & |6 f6 p6 M, L' _! _0 H: H. } ; p x a! a& I& V& e 9.1 General Device Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 `; I% `9 ?3 v7 }. } 9.1.1 Initialization of Device Internal Variables . . . . . . . . . 223$ b9 T5 [/ w/ n7 b' s 9.2 Devices as Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 W0 O' ^4 `! k8 T$ Y! S. G( K 9.2.1 Base Device Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228/ [( z w4 e* |, x6 T / d) ?. S) X" a5 v4 N) U' S- n. C 9.2.3 Specific Device Methods . . . . . . . . . . . . . . . . . . . . . . . . 241+ Q1 d0 n+ ]: u% F) W 10 Power Flow Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2474 s2 \& a4 M( d5 F, _2 p5 W 10.1 Topological Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247% U& I- V a. x# t6 E1 ?( i ( i' e! {, F- K9 v1 j 10.1.2 Areas, Zones, Regions and Systems . . . . . . . . . . . . . . . 2498 p" t, Y Y7 y$ \% Y0 J ; Z+ c4 ?9 p1 Z/ _ 1 D1 B3 Y9 n& P* y$ O4 l' k; F 9 F) j$ N" [9 ?# [ 10.2.3 PQ Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2565 ?. X& ]3 G- T+ Q- W- \ 10.3 Static Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257" K+ G& ^; j- ~' y: U8 Q $ ~ E; C3 b, p$ f8 `+ i 10.3.2 Constant Power Factor Load . . . . . . . . . . . . . . . . . . . . 2597 w# t# d+ l9 O6 V: r' G 10.3.3 Shunt Admittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260* P2 o) n2 q# i' M0 I 10.3.4 Switched Shunt Admittances . . . . . . . . . . . . . . . . . . . . 260& t. K' O% r& Q) V* _' ?' g d( E7 ]3 ~7 V" D7 n' N$ i 1 [# D2 q5 L. Q) B: Q3 E( h( |! G * a' n8 q; P% f0 e+ ~/ w 6 F7 l# `& c% Z; p# N0 H 11.1.2 Tie Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267/ H7 n" S, [9 s0 k; { l5 ?( X' h1 h% G 11.1.4 Effect of Frequency Variation . . . . . . . . . . . . . . . . . . . . 2703 N" p/ |) A0 A& K& [6 A # ~2 Z, T7 {+ }6 ? 11.2 Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 E. E d/ m% [" f" V" w 11.2.1 Two-Winding Transformer . . . . . . . . . . . . . . . . . . . . . . 272/ v, K$ m: ^# b6 L6 {# o- ^ 11.2.2 Under Load Tap Changer . . . . . . . . . . . . . . . . . . . . . . . 2757 t, ]# o/ O6 o, C; w; a+ I6 e3 I6 @ " R$ o8 s# d6 y! j * [" b: f! P' y% f 11.3 Vectorial Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282) J6 F4 A; P4 W9 B 8 L0 l2 x6 j9 I: e 11.3.2 Jacobian and Hessian Matrices . . . . . . . . . . . . . . . . . . 285' l: M, d# o7 Z" ?3 M( b' l. x l5 Y 8 ?/ C" {8 t, a0 w- M3 m7 l 12 OPF Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2918 t" q' n5 F: R0 o2 n 1 `+ U3 | m6 |5 a7 D 12.1.1 Bus Voltage Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2919 F! l( C3 T2 a4 A7 e- Q$ G! x' ?2 V " t2 f1 V4 n5 q # n& w! g' g! F8 E% t 12.2.1 Capability Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292' Q6 D# h% t; H3 ]+ D" y/ u3 r 12.2.2 Supply Offer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293+ B8 q- ?0 D4 q. Z 12.2.3 Reactive Power Payment Function . . . . . . . . . . . . . . . 296/ X7 ?2 s; k0 `6 F! c6 y 12.2.4 Generator Power Reserve . . . . . . . . . . . . . . . . . . . . . . . 298+ O1 ^, V2 m `7 ` 12.2.5 Generator Power Ramp . . . . . . . . . . . . . . . . . . . . . . . . . 299" \- W2 V) u ^6 p1 T. ? ) O9 g, z& R5 t+ P 1 L3 l" b) @ X/ V7 @ 12.3.2 Demand Daily Profile . . . . . . . . . . . . . . . . . . . . . . . . . . 302% P7 z: e- L( G. U, q4 E( x' I/ b 12.3.3 Demand Power Ramp . . . . . . . . . . . . . . . . . . . . . . . . . . 3034 s: h1 H3 |$ u- H/ B1 ] 7 Q5 [( K6 s! ? [2 O% P7 K% t E 13.1 Fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305' m2 P Y# J, W" X9 v 13.2 Breaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306. R: l0 m3 n: d9 X) T 13.3 Relay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3070 x* w/ k% g6 ? 13.4 Phasor Measurement Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309! j( ~/ D/ R: B7 r# u" `, [% P( l 13.5 Bus Frequency Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311' O. d( N& o) I9 [; K ! h$ `& ?0 \1 o8 C8 @4 [1 u6 x% L - `: z& Z- s+ V) [ 4 K( V+ A* f# R$ T, ~4 \ 14.3 Frequency Dependent Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3162 J5 R$ |9 ^: n- z1 g 14.4 Voltage Dependent Load with Dynamic Tap Changer . . . . . . 317# [0 |! P2 h/ x7 u& K" o 14.5 Exponential Recovery Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320/ \" w$ F- x; A: m 5 R. f9 `: K, d5 q& X, _2 U8 @ 14.6 Thermostatically Controlled Load . . . . . . . . . . . . . . . . . . . . . . . 321$ J0 q- C( n- ]% J! A- z B$ j 14.7 Jimma’s Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322' r8 r1 U, J% |, j( S3 X8 `4 t / d7 F3 n" x5 ?2 W0 ?% ]8 }0 @1 x 15 Alternate-Current Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 V4 E) N* c U7 t; B1 g 15.1 Synchronous Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325$ r3 N; n7 M" E$ x/ u+ ? 6 j2 [9 s5 g. F# y" m- x" _ 15.1.2 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327/ ~; ~) C3 d4 h# A / U" T, v( x( W% u7 v# c1 U E8 r7 w5 S$ g; w0 z" q 6 ?$ M& m, F; P6 u: z. c # j! }$ O5 `4 S! g 15.1.7 Synchronous Machine Model Taxonomy. . . . . . . . . . . 3360 ~1 ^& g' Y2 c: T X4 {' U 8 l3 A y- x& G# L0 P; `8 z1 Q! f 15.1.9 Center of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342* {% b. w* a6 ?+ [! ~8 L 15.1.10 Dynamic Shaft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343# W4 o u+ L9 Z2 t3 L2 S. i 15.1.11 Sub-synchronous Resonance . . . . . . . . . . . . . . . . . . . . . 3454 V2 }8 e$ C4 U7 E 15.2 Induction Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348* A D6 A" ?) `$ ?4 [1 t# e 15.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 z. e9 c9 H0 j$ v% h ' A& ?+ d3 b7 H% r; |* q8 V ) _* `" z) r6 w d* J/ G- | 4 [( o2 e* |# K- S$ k 15.2.5 Detailed Double-Cage Model . . . . . . . . . . . . . . . . . . . . 351& O: C) S, f" ^: P9 e- ^/ o 16 Synchronous Machine Regulators . . . . . . . . . . . . . . . . . . . . . . . . 355% }; x6 l. D _% A" Q: } % ?( u0 e, O3 W3 K n$ L# ?3 m4 Y ' l o( X3 F/ G- r) L 16.1.2 Turbine Governor Type II. . . . . . . . . . . . . . . . . . . . . . . 3594 M; N; V7 H9 f0 A; [# I: S 16.2 Automatic Voltage Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 361/ P6 M) t# A- T3 V + z- L* X) j+ z" ]% s$ d. K" k, ^ 16.2.2 Automatic Voltage Regulator Type II . . . . . . . . . . . . 3640 |9 E' J" W$ Q' x: Z% V" o 16.2.3 Automatic Voltage Regulator Type III . . . . . . . . . . . . 366: F! N- |! u# [$ _; W 16.3 Power System Stabilizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369" a$ r5 S) _* G1 k! s7 P/ D5 b 16.3.1 Simplified Power System Stabilizer Model . . . . . . . . . 3712 E. f" o2 F% o( L: ^6 ~ + X% A$ W* S6 e$ O' u9 b ' ?. l v9 t9 C& }# z 16.3.4 Power System Stabilizer Type III . . . . . . . . . . . . . . . . 373/ R y- x2 ?! k4 m: P6 R$ f" a # k: I2 m9 R8 B. Q 16.5 Under-Excitation Limiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376/ [ P% g! Z9 e. e9 ]8 v 9 D& U& g7 o8 g/ T; a4 x _9 ? M6 x T1 P A" K 6 C2 f! z$ Y1 l, T5 B9 B : V: A8 B6 c7 A) v 17.4 Basic RLC Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3820 q1 G$ I, s4 Z% r* N XX Contents2 N* M$ |3 _* F 17.5 Direct-Current Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384# @+ P! a2 A% N5 {& ^ $ v. V5 d% \' L& [: | + N6 C& @7 C. g: I " w" O5 }- X$ ~0 Y( F+ J 17.6.3 Battery Energy System . . . . . . . . . . . . . . . . . . . . . . . . . 3918 g( l! O! d- ~( Q + v6 d9 R: r0 t5 m: z2 O 18.1 High-Voltage Direct-Current Transmission System . . . . . . . . . 395 Q0 H0 N7 V2 F- d d* H! B 18.1.1 Per Unit System for DC Quantities. . . . . . . . . . . . . . . 3969 O) ?# p7 m4 y4 ?7 v 18.1.2 Rectifier Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3966 x i6 m2 Z, l# M& Y + t3 P: S' |* W5 F( { % d+ N7 F# x) r4 C0 f 18.2 Voltage Source Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4005 m$ K! w6 q: J7 |3 N 18.2.1 Simplified Dynamic VSC Model. . . . . . . . . . . . . . . . . . 408! X- `( F( u3 u/ a/ F) B9 l2 X 18.2.2 Power Flow VSC Model . . . . . . . . . . . . . . . . . . . . . . . . 409+ }5 I! `) L- p* m3 o% k 19 FACTS Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413$ k7 F. p8 A8 @ Z/ M* R& F 7 V; F2 `/ [2 M* h- v+ n( _9 S% I 19.1.1 SVC Type I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4139 K7 ?4 [$ @$ h* {6 E% E$ f 19.1.2 SVC Type II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4140 f3 j2 b/ f9 W( y 19.1.3 SVC Initialization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415( X9 K6 v2 i$ e: } 19.2 Thyristor Controlled Series Compensator . . . . . . . . . . . . . . . . . 4170 {& A& ~0 R2 e; R5 C2 K 19.2.1 TCSC Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4198 G" ~3 Q( Z6 F 19.3 Static Synchronous Compensator . . . . . . . . . . . . . . . . . . . . . . . . 419/ U _: k: l" W( W 19.3.1 Detailed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420- \$ T% k/ y5 y. G 19.3.2 Simplified Dynamic Model . . . . . . . . . . . . . . . . . . . . . . 421% T4 @7 g9 t% h' k9 J 19.3.3 Power Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4220 d- Z) d5 p! N+ k * k% g( S* q9 ~- B8 Q9 ? 19.4 Static Synchronous Series Compensator . . . . . . . . . . . . . . . . . . 423$ E; Q9 D0 f. q) y6 }) { 4 l& K6 D: Z7 [6 E5 L , `+ i/ D C/ F4 v% q 19.4.3 Power Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427, x, I( x* c1 G 5 d6 n" |6 B- C2 P: W 6 H/ j+ k; Z5 |* m 8 f @' V% [5 K 19.5.2 Simplified Dynamic Model . . . . . . . . . . . . . . . . . . . . . . 431) k5 c" y q1 s9 C0 e. k 19.5.3 Power Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433& M; G# v# O) m6 u + r/ M9 Z! r# k9 s9 Z: d( _ 3 O* v4 b$ J# U+ x 20.1 Wind Speed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435/ z$ H6 Y* N( S j ! n8 E* \1 o+ g) F0 f0 I ' P1 _, M2 [% e+ x, j8 y 3 e; U7 O3 \# p+ ^! G 20.2 Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440! X6 O5 U" J! x5 z$ z4 M* C: C3 J Contents XXI% [8 S, R4 }' ?7 M 20.2.1 Single Machine and Aggregate Models . . . . . . . . . . . . 441 n/ f# l9 i) L3 c: Z + P- M' @% ~7 U8 B 3 c5 T. d* u% z5 A8 d 20.2.4 Dynamic Shaft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4460 W2 v/ Q, t* X1 B/ Z2 K F- A 0 H1 W( j8 F! K# g( I 20.2.6 Doubly-Fed Asynchronous Generator . . . . . . . . . . . . . 449 U6 J0 e" p% Q 7 T: E) i3 b7 S! f1 A- n/ z' Q& x# b" D Part IV: Spare Material and Concluding Remarks# M% {5 D2 F( c! [* v 21 Data Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4598 P$ w9 G y7 q+ a9 X. [1 D3 r 21.1 Data Format Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4592 Q8 t$ Z) l; F" L ! c. I6 L' Y- q! `. A$ {, t : }& y) f3 t1 B* @4 t$ \6 t( F4 ^ 7 g% ]) B( [9 n2 b2 F5 R; l 7 M' D+ ~0 f5 K: f1 [ . n7 ~5 g) p- c. R3 Q # t h8 B' u; n* J7 ] j : T* G" o; U% b& L* k3 { # ^3 o- l; b% y+ i+ e5 k5 Y 2 V. B: S4 d( i7 ?* x# l0 X 7 c; H' Z# ` |4 |# S 7 ?4 `9 ~4 |; w+ v! W 22.2.1 Standard Two-Dimensional Plots . . . . . . . . . . . . . . . . 478& o9 _0 b- @6 t0 k+ s K' D 22.2.2 Temperature Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482# U/ P6 H+ b2 I5 H$ C . I2 m' S! q$ t 5 b: f" E# u3 X! U9 G # ]! C6 W, I# R' n) }0 b 9 ?+ w1 L/ w; c! _7 C" Q k, F: _' M H- v" V4 W1 O; N8 R+ I & V2 c* }( w7 {) S$ k6 q( A: H 23.1.3 Free Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490" B7 ^5 l9 U1 m / z/ F1 o' [% |7 @ 9 [) K+ _. S- }$ [: j% D d/ K : e+ j) t: N+ @0 I% t% U' _8 t8 K 8 t6 A/ L. o, W3 l; @1 L3 q 1 h- q- A4 W7 v! Y: s( @5 { Part V: Appendices$ z( X4 U9 F6 {2 G `9 B A Python Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497- p$ a+ m* s6 t4 f ( V7 h1 a* u: Y0 d# } . y, Y3 y4 M: T$ ^3 `5 z; L & x, b1 T; X$ z, d* D ) C5 L& q& F( f& R A.1.4 cvxopt.umfpack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5030 R% ?) ~5 S7 d" ]/ z6 P% @ ( y, q6 ]0 m1 M* Y! G/ l A.3 Matplotlib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5078 x5 D7 _! e! F 8 B9 h& _- U/ u( c" I) L/ ~ 3 r! u2 X5 P2 H6 ?: c% r ( d. h1 R% j! n f& J( @$ w$ C) r) n 9 R/ Z8 [7 [0 E. P 8 b& S( G: Z& G7 }1 t, V & H- ?5 \( p+ r+ Q: J " w% c$ R/ S x% j* |- J, r5 ? ; n+ L* \ v/ b - Q8 A/ i( u& w D.5 FACTS Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524" d9 M. @( P$ ^ / ~+ }+ a: k$ C" @9 x* e# F # M- c* n- }5 n4 {& }# c E.1 Software Packages Used in the Book . . . . . . . . . . . . . . . . . . . . . 529 ?- U1 O* [# H E.2 Links related to Power System Analysis . . . . . . . . . . . . . . . . . . 530' O7 ^. M1 }/ L/ m6 k3 B* E & k- k' U& |9 F5 J$ d0 x Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551/ v# [ A( |0 L x9 _8 J$ E 4 l2 e- U6 a. c0 M
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