Please copy and paste this embed script to where you want to embed

Dynamic Simulation of Basic Electrical Circuits using Matlab\Simulink

DRDO Sponsored Two days National Workshop Modern Power Simulation Tools MPST-10 Presented by Lenin Prakash.S

Objectives • Revisit System and Circuit Simulation • Describe how differential equation can be solved using Simulink • Simulating Basic electrical Circuits and Machines using their Mathematical Model

Contents •Introduction to Simulation using Mathematical Models •Solving a Differential Equation using Matlab\Simulink •Simulation of Basic Electrical Circuits •Simulation of PMDC Motor •Simulation of DC Shunt Motor •Simulation of 3-Phase Induction Motor •References

Expected Outcome • Solve a differential equation using Matlab\Simulink • Simulate basic electric circuits and DC machine • Learn to simulate all linear electrical circuits using their mathematical models by applying the same methodology

Introduction to Simulation using Mathematical Models

• In Broad 2 approaches are used in Simulating Electrical systems – Circuit Simulation – System Simulation

• System Simulation – Solving the differential equations representing the circuit – Solving the transfer function representing the circuit – State-Space Model approach

• Solving Differential Equation – Most of the electric circuit can be represented by it’s equivalent linear differential and algebraic equations – All electrical machines as such (without drives) can be modeled into a set of differential and algebraic equations – Simulation of power electronic circuits involves solving non-linear differential equation

Solving a Differential Equation using Matlab\Simulink

Differential Equation of a RL Circuit

di L + iR = V dt

di V − iR = dt L

V − iR i=∫ dt L

• Simulink Consists of different blocks for performing mathematical operations •To solve the above equation we need •Subtractor •Divider •Integrator •Constant (for representing V,R,L) •Simulink also Consist of a “Fcn” (function) block where the equation can be written which involves more than one operator ( +,x etc..)

Simulink Model for Solving a Differential Equation

•Simulink Blocks used in this model are •Constant – for representing V (O/p of this block is V) •Add/Subtractor – for performing V-IR (O/p of this block is V-IR) •Fcn- for performing (ir and (v-IR)/L) (O/p of this block is di/dt) •The i/p of this block is considered as u •Integrator – for integrating di/dt (O/p of this block is i)

Simulation of Basic Electric Circuits 1. RL Load fed by a DC Source 2. RC Load fed by a DC Source 3. RLC Load fed by a DC Source

Simulation of RL load Fed by a DC source R

L

V i(t)

Simulink Model of RL Circuit

di L + iR = V dt

Simulation of RC load Fed by a DC source R

C

V i(t)

Simulink Model of RC Circuit

1 ∫ i (t )dt + iR = V C

Simulation of RLC load Fed by a DC source R

L

C

V i(t)

Simulink Model of RLC Circuit

di 1 ∫ i (t )dt + L + iR = V C dt

Simulation of PMDC Motor

Differential Equations of a PMDC Motor dia + ia ra + Kωr = Va dt dω Te = TL + j r + Bωr dt Te = Kia LAA

M

Va

Eb = kωr

Typical parameters of a Dc shunt motor LAA = 120mH kT = 1.41×10 − 2 V .s / rad J = 1.06 ×10 −6 Kg .m 2 no _ load _ speed = 3350rpm = 351.1rad / s I a _ no _ load = 0.15 A

Simulink Model of PMDC Motor

Simulation of DC Shunt Motor

Differential Equations of a Dc shunt motor dia + ia ra + LAF i f ωr = Va dt di f + i f rf = V f LFF dt dω Te = TL + j r + Bωr dt LAA

M

Va

Typical parameters of a Dc shunt motor R f = 240Ω LFF = 120 H LAF = 1.8 Ra = 0.6Ω LAA = 0.012 H VDC = 240V J = 1Kg .m 2 I a _ rated = 16.2

ωr = 127.7rad / s

Simulink Model of DC Shunt Motor

Simulation of 3-Phase Induction Motor

Equivalent circuit of 3-Phase Induction Motor

Differential Equations of 3-Phase Induction Motor

Flux Linkage Equations

Algebraic Equations of 3-Phase Induction Motor Stator Current Equations

Rotor Current Equations

Torque/Speed Equations

Typical Parameters of a 3-Phase Induction Motor

Block Diagram for Simulation of 3-Phase Induction Machine in Arbitrary Reference Frame

Simulink model of 3-Phase Induction Machine in Arbitrary Reference Frame

References

•Analysis of electrical machinery and drives system- Paul C.Krause, Oleg wasynczuk,Scott D.sudhoff

Questions ?

Thank You

View more...
DRDO Sponsored Two days National Workshop Modern Power Simulation Tools MPST-10 Presented by Lenin Prakash.S

Objectives • Revisit System and Circuit Simulation • Describe how differential equation can be solved using Simulink • Simulating Basic electrical Circuits and Machines using their Mathematical Model

Contents •Introduction to Simulation using Mathematical Models •Solving a Differential Equation using Matlab\Simulink •Simulation of Basic Electrical Circuits •Simulation of PMDC Motor •Simulation of DC Shunt Motor •Simulation of 3-Phase Induction Motor •References

Expected Outcome • Solve a differential equation using Matlab\Simulink • Simulate basic electric circuits and DC machine • Learn to simulate all linear electrical circuits using their mathematical models by applying the same methodology

Introduction to Simulation using Mathematical Models

• In Broad 2 approaches are used in Simulating Electrical systems – Circuit Simulation – System Simulation

• System Simulation – Solving the differential equations representing the circuit – Solving the transfer function representing the circuit – State-Space Model approach

• Solving Differential Equation – Most of the electric circuit can be represented by it’s equivalent linear differential and algebraic equations – All electrical machines as such (without drives) can be modeled into a set of differential and algebraic equations – Simulation of power electronic circuits involves solving non-linear differential equation

Solving a Differential Equation using Matlab\Simulink

Differential Equation of a RL Circuit

di L + iR = V dt

di V − iR = dt L

V − iR i=∫ dt L

• Simulink Consists of different blocks for performing mathematical operations •To solve the above equation we need •Subtractor •Divider •Integrator •Constant (for representing V,R,L) •Simulink also Consist of a “Fcn” (function) block where the equation can be written which involves more than one operator ( +,x etc..)

Simulink Model for Solving a Differential Equation

•Simulink Blocks used in this model are •Constant – for representing V (O/p of this block is V) •Add/Subtractor – for performing V-IR (O/p of this block is V-IR) •Fcn- for performing (ir and (v-IR)/L) (O/p of this block is di/dt) •The i/p of this block is considered as u •Integrator – for integrating di/dt (O/p of this block is i)

Simulation of Basic Electric Circuits 1. RL Load fed by a DC Source 2. RC Load fed by a DC Source 3. RLC Load fed by a DC Source

Simulation of RL load Fed by a DC source R

L

V i(t)

Simulink Model of RL Circuit

di L + iR = V dt

Simulation of RC load Fed by a DC source R

C

V i(t)

Simulink Model of RC Circuit

1 ∫ i (t )dt + iR = V C

Simulation of RLC load Fed by a DC source R

L

C

V i(t)

Simulink Model of RLC Circuit

di 1 ∫ i (t )dt + L + iR = V C dt

Simulation of PMDC Motor

Differential Equations of a PMDC Motor dia + ia ra + Kωr = Va dt dω Te = TL + j r + Bωr dt Te = Kia LAA

M

Va

Eb = kωr

Typical parameters of a Dc shunt motor LAA = 120mH kT = 1.41×10 − 2 V .s / rad J = 1.06 ×10 −6 Kg .m 2 no _ load _ speed = 3350rpm = 351.1rad / s I a _ no _ load = 0.15 A

Simulink Model of PMDC Motor

Simulation of DC Shunt Motor

Differential Equations of a Dc shunt motor dia + ia ra + LAF i f ωr = Va dt di f + i f rf = V f LFF dt dω Te = TL + j r + Bωr dt LAA

M

Va

Typical parameters of a Dc shunt motor R f = 240Ω LFF = 120 H LAF = 1.8 Ra = 0.6Ω LAA = 0.012 H VDC = 240V J = 1Kg .m 2 I a _ rated = 16.2

ωr = 127.7rad / s

Simulink Model of DC Shunt Motor

Simulation of 3-Phase Induction Motor

Equivalent circuit of 3-Phase Induction Motor

Differential Equations of 3-Phase Induction Motor

Flux Linkage Equations

Algebraic Equations of 3-Phase Induction Motor Stator Current Equations

Rotor Current Equations

Torque/Speed Equations

Typical Parameters of a 3-Phase Induction Motor

Block Diagram for Simulation of 3-Phase Induction Machine in Arbitrary Reference Frame

Simulink model of 3-Phase Induction Machine in Arbitrary Reference Frame

References

•Analysis of electrical machinery and drives system- Paul C.Krause, Oleg wasynczuk,Scott D.sudhoff

Questions ?

Thank You

Thank you for interesting in our services. We are a non-profit group that run this website to share documents. We need your help to maintenance this website.

To keep our site running, we need your help to cover our server cost (about $400/m), a small donation will help us a lot.