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 Take Aways

• Elevator Speech understanding of Synchronous Generator Dynamic

Machine Model

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

• 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

( ) cos( )

m

x t X t ω φ = +

[cos sin ] 2

m

X X j φ φ   = +    

Synchrophasor Computation

1 1 1cos 1 1sin 2 2 1sin 1 1cos 1sin 1cos 1sin 1cos

2 {cos( ) sin( )} 2 cos(1 ) 1 fundamental frequency 2 sin(1 ) arctan

N k n N n N n n n n

X k n j k n N X n N k X n N X X X j X X X X x x x θ θ θ θ

∑ ∑ ∑

− = − = − =

= −  =   =   =     − = − ⇒ + ∠    

Phasor Measurement Unit – System Model

Synchronous Machine

b b b s a c s c c s a a

d d v d v i r v i r d d t t t i r d λ λ λ = + + = + =

1 1 1 1 2 2 2 1 1 1 2 1 fd fd fd fd d d q q q q d q d q q q

d v i r dt d v d v i r dt d v i r dt i r dt λ λ λ λ = + = + = + = +

Stator Rotor

• r

,

d a q dqo b c

• v

v v T v i v v λ         ∆            

Synchronous Machine

1 1 1 1 2 2 2 1 1 1 2 1 fd fd fd fd d d q q q q d q d q q q

d v i r dt d v d v i r dt d v i r dt i r dt λ λ λ λ = + = + = + = +

Stator Rotor

q q s q d d s d q

• s

d

• d

v r d d v v r i d r i t t dt d i λ ω λ λ λ ωλ = + + + = = + −

Dynamic Phenomena Time Scales

Mechanical Electrical

Shaft Dynamics

( ) ( )

1 sin 1 c (5.42) (5.43) (5.44)

• s

de se d t qe s vs s qe se q t de s v s s e s

• e
• d

R I V dt T d R I V dt T d R I dt ψ ε ε ω ψ ψ δ θ ψ ε ε ω ψ θ ε δ   = + + + −       = − + + −  =   

3 Fast Dynamic States

, ,

de qe

• e

ψ ψ ψ

( )

d ep de d de ed p ed d e

X I X X X ψ ψ ψ ψ = + = − = +

( )

q ep qe q qe eq p eq q e

X I X X X ψ ψ ψ ψ = + = − = +

( ) ( ) ( )

( )

( )

1 2 1 1

(5.45) (5.46)

q d d do q d d d d d s d q fd d s d do d q d s d

dE X X T E X X I X X I E E dt X X d T E X X I dt ψ ψ ψ   ′ ′ ′′ − ′ ′ ′ ′ ′   = − − − − + − − + ′  −    ′′ ′ ′ = − + − −

  



( ) ( ) ( )

( )

( )

2 2 2 2

(5.47) (5.48)

q q d qo d q q q q q s q d q s q qo q d q s q

X X dE T E X X I X X I E dt X X d T E X X I dt ψ ψ ψ   ′ ′′ − ′   ′ ′ ′ ′ ′ = − + − − + − +   ′ −   ′′ ′ ′ = − − − −

  



11 not so fast Dynamic States (1/2)

1 2

, , , , ,

q d d q t

E E ψ ψ δ ω ′ ′

Synchronous Generator ( )

(5.49) (5.50)

s t q qe t s M d d W e F

d T dt d T T I T t I d ψ δ ω ω ψ = = − − −

1

( )

q

ψ ∝ ( )

fd

ψ ∝

11 not so fast Dynamic States (2/2)

,

m SV

T P

( )

(5.54) (5.55) (5.56)

E E F F F f f A F R R fd fd fd fd t R A F f A A

ref

d T K dt d K T dt T d E E K E K T K K V V V V V dt R R T R E = − + = − + = − + − + −

Main Exciter Stabilizing Transformer Pilot Exciter Excitation System

, ,

fd f R

E R V

(5.63) (5.64)

SV CH SV C D s SV SV M M t

P P T T d T dt d T P dt R T P ω ε = − + = − + −

Mechanical Power System Single Stage Turbine Model Governor Model

• PSV = Steam Valve Psn ( Pressure)
• PC = Power change setting
• PC = 0 when Open Ckt
• RD = Speed Droop Regulation Qty

(Terminal Voltage Control) (Shaft Speed Control)

% Full Model

• ptions = odeset('Mass‘,Mass_Matrix,

MaxOrder',5,'MaxStep',.002); [Full_Mdl_Soln] = ode15s(@Full_Model, tspan,Init_Cond,options);

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) T_qoprime; %( 6)T_qoprime T_qo2prime; %( 7)T_qo2prime T_A; %(12)T_A 0.0; %(18)Algebraic Eqn (V_t) 0.0; %(19)Algebraic Eqn (V_d) 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

Terminal Voltage Dynamic Response – abc frame

1 a d b dqo q c

• v

v v T v v v

−

        =            

Terminal Voltage Dynamic Response

1 a d b dqo q c

• v

v v T v v v

−

        =            

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