Notes Power System Dynamics and Stability

Slides:



Advertisements
Similar presentations
ECE 576 – Power System Dynamics and Stability
Advertisements

Submitted by: Name:Rajendra Kumar Choudhury Branch:Electrical Engg.
Chapter 4 Synchronous Generators
Two-pole,3-phase,wye-connected,salient-pole synchronous machine
Modeling of Induction Motor using dq0 Transformations
ECE Electric Drives Topic 4: Modeling of Induction Motor using qd0 Transformations Spring 2004.
Topic 5: Dynamic Simulation of Induction Motor Spring 2004 ECE Electric Drives.
ECE 4411 Induction Generators Same basic construction as squirrel-cage induction motors Drive at a speed greater than the synchronous speed Not started.
Synchronous Generator
Announcements Be reading Chapter 11 and Chapter 12 thru 12.3
Department of Electrical and Computer Engineering
Module G1 Electric Power Generation and Machine Controls
Unit 5 An Introduction to Mechanical Engineering: Part One Electrical and Electronic Systems 5.2 – key points Kirchhoff postulated that in any circuit.
Lecture 32Electro Mechanical System1 Assignment 9 Page 373 Problems 16-13, 16-16, and Due Date: Tuesday 19 th April, 2011 Quiz No.5 Next Week Quiz.
Southern Taiwan University of Science and Technology
Dynamic Model of Induction Machine MEP 1522 ELECTRIC DRIVES.
EET 306 ELECTRIC MACHINES Syafruddin Hasan.
ECE 576 – Power System Dynamics and Stability
Protection & Switchgear
Lecture 9: Modeling Electromechanical Systems 1.Finish purely electrical systems Modeling in the Laplace domain Loading of cascaded elements 2.Modeling.
ECE 576 – Power System Dynamics and Stability Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign.
ECE 576 – Power System Dynamics and Stability
Dynamic Model of Induction Machine. WHY NEED DYNAMIC MODEL? In an electric drive system, the machine is part of the control system elements To be able.
Control Engineering. Introduction What we will discuss in this introduction: – What is control engineering? – What are the main types of control systems?
Prepared by:- Chandan pathak ( ) Utpal rathod( ) Hitendra vyas( )
Presentation of ELECTRIC MACHINES Title: Single Phase Motors By: Rahul Khanna{ }EC3 rd Sem Guided By: Prof. Ravi Patel.
ECE 576 – Power System Dynamics and Stability
Lesson 12a: Three Phase Induction Motors
EE Iowa State University
SYNCHRONOUS GENERATOR
ELECTRICAL MACHINES Electrical Machines.
Chapter 5: Speed-Torque Characteristics of Electric Motors
Components Motors and Generators.
Components Motors and Generators.
Speed control of three phase induction motor
ECE 476 Power System Analysis
Electric Machine Induction Motor
Why are the transmission lines high-voltage, three-phase and AC?
Principle of Operation
Induction Generators Same basic construction as squirrel-cage induction motors Drive at a speed greater than the synchronous speed Not started as a motor.
Background Motor Description: 13.2kv, 7000hp, 3600rpm, FLA=253, LRA = 1563A Performed simulation by interrupting at current zero’s. A first, then B/C.
ECEN 460 Power System Operation and Control
Wind turbine technology
Synchronous Motors and Generators
Presentation of ELECTRIC MACHINES Title: Single Phase Motors By: Rahul Khanna{ }EC3 rd Sem Guided By: Prof. Ravi Patel.
Lecture 41 Selective Eigenvalue Analysis in Power Systems Professor M.A. Pai Department of Electrical and Computer Engineering © 2000 University of Illinois.
Advanced Power Systems
ECEN 460 Power System Operation and Control
EE216 Electrical Engineering
ECE 476 POWER SYSTEM ANALYSIS
Principle of Operation
Think beyond.
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECEN 667 Power System Stability
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
ECEN 667 Power System Stability
ECEN 667 Power System Stability
ECEN 667 Power System Stability
Chapter 25 Elements of Electromechanical Energy Conversion.
ECE 576 POWER SYSTEM DYNAMICS AND STABILITY
Electric Machine Design Course
Presentation transcript:

Notes Power System Dynamics and Stability Prepared by Karl Reinhard reinhardke@gmail.com Latest Update: 1 Feb 18 Supporting PhD Dissertation: Power System Dynamic Modeling and Synchrophasor Measurements ©Jan ‘17 Based upon Power System Dynamics and Stability Peter W. Sauer and M.A. Pai 1st Edition Contents Variables and Definitions 1 Single Machine, Inf Bus, Balanced 3f Transmission Line (T.L.) 4 Reference Frame Theory Prep to consider Unbalanced 3f T.L. 6 Park’s Transformation for Resistive T.L. Component 8 Park’s Transformation for Inductive T.L. Component 9 Eqn Dev for Stator Components 10 Eqn Dev for T.L. Components 11 Modified Eqns for d and q formulation 13 Transmission Line Eqn Development 18 Single Machine, Inf Bus, Un-Balanced 3f Transmission Line (T.L.) 20 Single Machine, Resistive Load (Raskin), Eqn Development 27 Single Machine, Resistive Load (Raskin), Eqn Development ( = 0) 29 4/8/2019

Variables and Definitions 4/8/2019

Variables and Definitions (cont) 4/8/2019

Single-Machine-Infinite Bus (Generator Notation) Differentiate Id and Iq to find explicit expression for evaluating Vd and Vq Combined Flux terms incl. Machine & Trans. Line 3 Fast Dynamic States (1) (2) (3) 11 not so fast Dynamic States (4) (5) (6) (7) (8) (9) Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 6 Algebraic States (13) 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 e = 2p (60) retained to preserve governor function (15) (14) (16) (17) (18) (19) (20) 4/8/2019

Algebraic Steps leading to eqns (5.51.3) and (5.52.3) 4/8/2019

3f Breaker Opening – Referring Re and Xep into Rotor Frame Single-Machine-Infinite Bus (Generator Notation) 3f Breaker Opening – Referring Re and Xep into Rotor Frame 3 Fast Dynamic States (1) (2) (3) Reference Frame Theory 3 Fast Dynamic States – Unbalanced Conditions (Note: Unbalanced TL conditions do not allow combining machine and TL terms into compact Yde terms as in 5.42 – 5.44) (1) (2) (3) 4/8/2019

6 Algebraic States (15) (16) (17) (19) (20) 4/8/2019

Park’s Transformation – Resistive Component Lumped Parameters Krause: Except for isolated operation, it is convenient for analysis and interpretation purposes to related the SM rotor position to a reference voltage (or to another machine in a multiple machine system). The rotor angle, d , is defined as the electrical angle displacement between the rotor and its terminal voltage. (p207) 4/8/2019

Park’s Transformation – Inductive Component 4/8/2019

Equation Development Stator Components: (3.1) (3.2) (motor current notation) (3.3) Apply Park Transformation to refer “stator frame” variables and constituent relations to “rotor frame” : (3.17) (3.18) (3.19) (motor current notation via ‘-’ in scaling factor) (3.148) (3.149) (3.150) Note the dqo Transformation eliminates yo term in the dqo frame 4/8/2019

Equation Development Transmission Line Components: (3.27) (3.28) (3.29) Apply Park Transformation to refer TL “stator frame” variables and constituent relations to “rotor frame” : TL treated as lumped parameters with mutual cross inductance (3.17) (3.18) (3.19) 4/8/2019

Equation Development Transmission Line Components (cont) : 6 Algebraic States (5.59.2) (5.60.2) The ‘–’ arises because the scaling converts ‘motor’ notation; however, the transmission line sign convention is preserved… ( Eqns 5.61 & 5.62) Distinguishing eqns 5.59 & 5.59.2 and 5.60 & 5.60.2 Park Transform of Balanced 3f X is diagonal 4/8/2019

MODIFIED (5.59.2) (1) (5.60.2) (2) (3) (1) (2) (3) (3.150.1) 4/8/2019

MODIFIED 4/8/2019

MODIFIED (1) (2) (3) 4/8/2019

4/8/2019

(1) (2) (3) 4/8/2019

4/8/2019

4/8/2019

Nom Voltage: 230 KV R (W/km) .050 XL = wL (W/km) .488 Bc = wC (ms/km) (Note the similarity of off-diagonal terms to balanced transmission line under normal conditions. Balanced neutral  Phase Currents sum to 0 Elgerd, Sect. 6-4-7, p 182. ) Compute Transmission Line Parameters for simulated case based upon Kundur’s Typical Transmission Lines, Table 6 Assume that D (phase conductor separation) is 5 meters; Determine R (conductor radius) to obtain Kundur’s value. Assume that D = Dn (effective distance from neutral to phase conductors – achieved via transposition) Assume that Rn = 1/3 R Nom Voltage: 230 KV R (W/km) .050 XL = wL (W/km) .488 Bc = wC (ms/km) 3.371 Zc = (W) 380 SIL (MW) 140 4/8/2019

SYNCHRONOUS MACHINE – INFINITE BUS (Generator Notation) Explicitly Modeled || Transmission Lines 3f Breaker Opening – Referring Re and Xep into Rotor Frame Updated 17 Oct 16 Font colors updated 8 Dec 16 3 Fast Dynamic States (1) (2) (3) 11 not so fast Dynamic States (4) (5) (6) (7) (8) (9) Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 15 Algebraic States (13) 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 e = 2p (60) retained to preserve governor function (14) (18) (19) (20) (15) (16) (17)

SYNCHRONOUS MACHINE – INFINITE BUS (Generator Notation) Explicitly Modeled || Transmission Lines 3f Breaker Opening – Referring Re and Xep into Rotor Frame Updated 17 Oct 16 Font colors updated 8 Dec 16 3 Fast Dynamic States 5.42.2) 5.43.2)   5.44.2) 11 not so fast Dynamic States Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 15 Algebraic States (13) 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 e = 2p (60) retained to preserve governor function (14) (18) (19) (20) (15) (16) (17)

KVL Equation TL 1 (Updated 20 Oct 16) (26) (27) (28) (21) (22) (23) KVL Equation TL 1 (Updated 20 Oct 16) (18) (5.59.3) (19) Null Source … … Null Source (5.60.3) (20) Null Source … … Null Source (25) (5.33)

 = 0 INDUCTOR: Null Source INDUCTOR: (1) (2) 4/8/2019  = 0 4/8/2019

P Q R S 25 Inductor, Transformer V Vterm VR Model Scaling Inductor, Speed V scaled w S 4/8/2019

KVL Equation TL 2 (5.59.4) (5.60.4) (5.33) 4/8/2019 (19.1) (20.1) (25.1) (30) (31) (24) (Theta shaft) (21.1) (22.1) (23.1) 4/8/2019

11 not so fast Dynamic States Single-Machine-Resistive Load (Raskin) model, Bus (Generator Notation) Full Model (e≠ 0) 3 Fast Dynamic States (1) (2) (3) 11 not so fast Dynamic States (4) (5) (6) (7) (8) (9) Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 6 Algebraic States (13) 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 e = 2p (60) retained to preserve governor function (15) (14) (16) (17) (18) (19) (20) 4/8/2019

11 not so fast Dynamic States Single-Machine-Resistive Load (Raskin) model, Bus (Generator Notation) Full Model (e≠ 0) and open ckt (I’s = 0) 3 Fast Dynamic States (1) (2) (3) 11 not so fast Dynamic States (4) (5) (6) (7) (8) (9) Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 6 Algebraic States (13) 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 e = 2p (60) retained to preserve governor function (15) (14) (16) (17) (18) (19) (20) 4/8/2019

11 not so fast Dynamic States Single-Machine-Resistive Load (Raskin) model, Bus (Generator Notation) -- Reduced Model (e = 0 ) 3 Fast Dynamic States (1) (2) (3) 11 not so fast Dynamic States (4) (5) (6) (7) (8) (9) Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 6 Algebraic States Single Stage Turbine Model (13) Governor Model * PSV = Steam Valve Psn ( Pressure) PC = Power change setting PC = 0 when Open Ckt RD = Speed Droop Regulation Qty e = 2p (60) retained to preserve governor function (15) (14) (16) (17) (18) (19) (20) 4/8/2019

11 not so fast Dynamic States Single-Machine-Resistive Load (Raskin) model, Bus (Generator Notation) -- Reduced Model (e = 0 ) and open ckt (I’s = 0) 3 Fast Dynamic States (1) (2) (3) 11 not so fast Dynamic States (4) (5) (6) (7) (8) (9) Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 6 Algebraic States Single Stage Turbine Model (13) (15) Governor Model * PSV = Steam Valve Psn ( Pressure) PC = Power change setting PC = 0 when Open Ckt RD = Speed Droop Regulation Qty e = 2p (60) retained to preserve governor function (14) (16) (14.1) (17) (18) (Ransick modeling problem statement) Vd and Vq are not defined for open Ckt (I’s = 0) and (e = 0); No P or Q powerflow and hence no reference angle (19) (20) 4/8/2019

11 not so fast Dynamic States Single-Machine-Resistive Load (Raskin) model, Bus (Generator Notation) -- Reduced Model (e = 0 and Open Circuit (I’s = 0 ) and Open Ckt assumptions Vd, yqe = 0 ) 3 Fast Dynamic States (1) (2) (3) 11 not so fast Dynamic States (4) (5) (6) (7) (8) (9) Excitation System (10) Main Exciter (11) Stabilizing Transformer (12) Pilot Exciter Mechanical Power System 6 Algebraic States (13) Single Stage Turbine Model (15) (14) Governor Model * *(PC = 0 when Open Ckt) (16) (17) (18) (19) (20) 4/8/2019