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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

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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

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