ECE ILLINOIS Karl rlReinh nhar ard Graduate Student - PowerPoint PPT Presentation

ECE ILLINOIS Karl rlReinh nhar ard Graduate Student Investigating Synchrophasor Data to Record Generator Equilibrium State Transitions Power and Energy Area Graduate Seminar 19 Oct ‘15

Purpose To Investigate Phasor data usefulness for Capturing system transient behavior between significantly different equilibrium states

Purpose To Investigate Phasor data usefulness for Capturing system transient behavior between significantly different equilibrium states Take Aways • Elevator Speech understanding of Synchronous Generator Dynamic Machine Model • MatLAB Tools Used • Simulation Results • Signal Processing Challenges

Outline • Synchrophasor Computation Description • Synchronous Generator Multi-Time-Scale Model Description • MATLAB -- Useful Tools • Simulation Results • Signal Processing Results • Future Directions

Synchrophasor Concept   X = φ + φ m   X [cos j sin ]   2 = ω + φ ( ) cos( ) x t X t m

Synchrophasor Computation 2 − N 1 = θ − θ X x {cos( k n ) j sin( k n )} ∑ k n = N n 0  2 − N 1 = θ  X x cos(1 n ) ∑  1cos n = N n 0 =  k 1 fundamental frequency  2 − 1 = N θ X x sin(1 n ) ∑  1sin n  = N n 0   − X = − ⇒ + ∠ 2 2 1sin   X X j X X X arctan 1 1cos 1sin 1cos 1sin   X 1cos

Phasor Measurement Unit – System Model

Synchronous Machine Rotor Stator λ d = + λ fd v i r d = + fd fd fd a v i r dt a a s d t λ d = + 1 d λ v i r d 1 1 1 d d d = + dt b v i r b b s λ d t d = + 1 q λ v i r d 1 q 1 q 1 q   = +   dt c v i r v v c c s d a λ   d t   d ∆ λ = + 2 q v T v or i , v i r     2 q 2 q 2 q q dqo b dt       v   v c o

Synchronous Machine Rotor λ d = + fd v i r Stator fd fd fd dt λ λ d d = + 1 d = − ωλ + v i r d v r i 1 d 1 d 1 d d s d q dt dt λ λ d d = + 1 q = + ω λ + q v i r v r i 1 q 1 q 1 q q s q d dt d t λ λ d d = + = + 2 q o v r i v i r o s o 2 q 2 q 2 q d t dt

Dynamic Phenomena Time Scales Electrical Shaft Dynamics Mechanical

3 Fast Dynamic States ψ ψ ψ , , de qe oe   ψ ε d ( ) ε = + + ω ψ + δ − θ de   (5.42) R I 1 V sin ψ = ψ + ψ se d t qe s vs   dt T s de d ed ( ) ψ   ε ψ = − d ( ) X I ε qe = − + ω ψ + δ − θ   (5.43) R I 1 V c os ed ep d se q t de s v s   dt T = + s X X X de d e p ψ d ε = oe (5.44) R I s e o dt ψ = ψ + ψ qe q eq ( ) ψ = − X I eq ep q = + X X X qe q e p

11 not so fast Dynamic States (1/2) ∝ ψ ∝ ψ ( ) ( ) fd 1 q ′ ′ ψ ψ δ ω Synchronous Generator , , , , , E E q 1 d d 2 q t   ′ ′ ′′ − ( ) dE ( ) X X ( ) ′ ′ ′ ′ ′ q = − − −  − ψ + − −  +  d d (5.45) T E X X I X X I E E  ( ) do q d d d 1 d d s d q fd ′ 2  −  dt  X X   d s ψ d ( ) ′′ ′ ′ = − ψ + − − 1 d (5.46) T E X X I  do 1 d q d s d dt   ′ ′′ − ′ ( ) ( ) ( ) X X dE   ′ ′ ′ ′ ′ = − + − − q q ψ + − +  d (5.47) T E X X I X X I E ( )    qo d q q q 2 q q s q d 2 ′ − dt X X    q s ψ ( ) d ′′ ′ ′ 2 q = − ψ − − − (5.48) T E X X I  qo 2 q d q s q dt δ d = ω (5.49) T dt s t ω ( ) d = − ψ − ψ − t (5.50) T T I I T s M d e q qe d F W d t

11 not so fast Dynamic States (2/2) E , R , V (Terminal Voltage Control) Excitation System fd f R d E = − + fd Main Exciter (5.54) T K E V E E fd R dt d R K = − + f F Stabilizing Transformer (5.55) T R E F f fd dt T F ( ) d V K K = − + − + − Pilot Exciter R A F (5.56) T V K R E K V V A R A f fd A ref t dt T F T , P Mechanical Power System (Shaft Speed Control) m SV d T = − + Single Stage Turbine Model M (5.63) T T P CH M SV dt Governor Model ε d P = − + − ω SV (5.64) T P P • P SV = Steam Valve Psn (  Pressure) SV SV C t dt R T • P C = Power change setting D s • P C = 0 when Open Ckt • R D = Speed Droop Regulation Qty

MATLAB Application  Solver ODE solver – ode15s – Stiff Differential-Algebraic Equations; variable time-step – variable order method Mass_Vector = [ T_s; %( 9)2*H/(2*pi*60) % Full Model T_qoprime; %( 6)T_qoprime options = odeset('Mass‘,Mass_Matrix, T_qo2prime; %( 7)T_qo2prime MaxOrder',5,'MaxStep',.002); T_A; %(12)T_A 0.0; %(18)Algebraic Eqn (V_t) [Full_Mdl_Soln] = ode15s(@Full_Model, 0.0; %(19)Algebraic Eqn (V_d) tspan,Init_Cond,options); 0.0 %(20)Algebraic Eqn (V_q) T_doprime; %( 4)T_doprime T_do2prime; %( 5)T_do2prime 0.0; %( 2)Reduced Sys Alg Eqn 0.0; %( 1)Reduced Sys Alg Eqn 0.0; %(15)Algebraic Eqn (I_d) 0.0; %(16)Algebraic Eqn (I_q)…

MATLAB’s DAE Structural Analysis Tool  MATLAB’s DAESA Tool – Differential-Algebraic Equations Structural Analyzer, – Determines structural index, number of degrees of freedom, constraints, variables to be initialized, and suggests a solution scheme.  MATLAB’s DAESA Tool – Structural index – # degrees of freedom – Constraints – Variables to be initialized, – Suggests solution scheme.

Machine Flux Linkage Dynamic Response

Machine Dynamic Frequency Response

Excitation System Dynamic Response

Mechanical System Dynamic Response

Terminal Voltage Dynamic Response – dqo

Terminal Current Dynamic Response

    v v a d     = Terminal Voltage Dynamic Response – abc frame − 1 v T v     b dqo q       v   v c o

    v v a d Terminal Voltage Dynamic Response     = − 1 v T v     b dqo q       v   v c o

Synchrophasors Off Fundamental Frequency Phadke, Arun G., and John Samuel Thorp. Synchronized phasor measurements and their applications. Springer Science & Business Media, 2008.

Synchrophasor Measurement During a Disturbance Phadke, Arun G., and John Samuel Thorp. Synchronized phasor measurements and their applications. Springer Science & Business Media, 2008.

Future Directions • Signal Processing -- Compute Simulated Phasor Measurement • Use RTDS (Real Time Digital Simulator) – Analog Response Simulation  Capture Phasor Measurements from Equipment • Answer the Question “Utility of Using Synchrophasor Data to Capture Power System Dynamics??”

QUESTIONS? Karl Reinhard reinhrd2@illinois.edu