Download Chapter 5 Switching Function, Circuit Models, and Simulation

Chapter 5 Switching Function, Circuit
Models, and Simulation
• Switching Function
– Use “0” and “1” to express a switch: switching function
– Use switching function to express voltage and current
relationships
• Circuit Models Based on Switching Function
– Examples to use switching function
• Simulation Using Switching Function Based Circuit
Models
August 15, 2003
F. Z. Peng: Slide 1
What is Power Electronics? My Definition
Idc
S1
S3
iac
From Chapter 1
Vdc
t
ON: 1
Load vac
Vdc
S2
S4
Voltage-Source Inverter
vac = (S1−S3)Vdc
Idc = (S1−S3)iac
Where S1, S3 = 0, 1
switching function
OFF:0
S1, S4
t
1
0
S2, S3
t
Fundamental
vac
t
1
vac
(PWM)
t
0
Waveforms of Inverter
• Power electronics is mega-processor for power (energy)
August 15, 2003
F. Z. Peng: Slide 2
The Basic Switching Cells
• All power electronics circuits are based on two simple
switching cells shown below and are a combination of
the basic switching cells.
From Chapter 2
Connect to the positive of a voltage-source or capacitor
Connect to a current-source or inductor with
the current direction shown
Connect to the negative of a voltage-source or capacitor
August 15, 2003
F. Z. Peng: Slide 3
Basic Control Theory of PE Circuits -Summary
V1
1
V0
S
0
V2
V0 = S ⋅ V1 + (1 − S ) ⋅V2
VL
Filtering element
Load
From Chapter 3
VL = V 0 = d ⋅ V1 + (1 − d ) ⋅ V2 , where d is the duty cycle
or the average of S over one switching cycle.
August 15, 2003
F. Z. Peng: Slide 4
Switching Function and V&I Relations
V1
I1
1
To capacitive terminal
v0
S
inductive element
i0
0
V2
I2
Use “0” and “1” to express a switching cell’s switching and
Express voltage and current relationships as follows:
v0 = S ⋅ V1 + (1 − S ) ⋅ V2 and
I1 = S ⋅ i0 , I 2 = (1 − S ) ⋅ i0
August 15, 2003
F. Z. Peng: Slide 5
Circuit Model for Switching Cell
I1
V1
1
Si0
v0
i0 v0
S
i0
0
V2
I2
Switching Cell
V2
(1-S)i0
SV1+(1-S)V2
V1
Circuit Model
August 15, 2003
F. Z. Peng: Slide 6
Example: Using Switching Function to
Model a Buck Converter Circuit
August 15, 2003
F. Z. Peng: Slide 7
Example: Using Switching Function to
Model 3-P Inverter Circuit
August 15, 2003
F. Z. Peng: Slide 8
Example: Using Switching Function to
Simulate 3-P Inverter Circuit
idc
Va
Vb
Vc
Vdc=350V
3mH ia
VLa
ib
VLb
ic V
Lc
Pspice schematic using
switching function model
4Ω
Va_ref
Va_ref
VdcSa
Sa
Vb_ref
Vc_ref
Vcarrier
Va
Vb_ref
Sb
Sc
1
Vc_ref
Sa
0
VdcSb
3mH ia
Vb
ib
Vc
ic V
Lc
VdcSc
VLa
VLb
4Ω
Vcarrier
Pspice Schematic Using
Ideal switches
Vdc
VdcSa
0
August 15, 2003
F. Z. Peng: Slide 9
Features:
Using Switching Function to Simulate
• Always converge
• Fast computation
• Good accuracy
• Easy analysis
• Easy design
August 15, 2003
F. Z. Peng: Slide 10