Shaghayegh Kazemlou
Advanced
Mechanical Design
Advisor: Dr.
Shahab Mehraeen
December 2008
Louisiana State University

Part I: Grid-connected Renewable System

Part II: Converter Discrete-Time Model

Part III: Converter Discrete-time Control Design

Part IV: Simulation Results

Part V: Summary and Future Works
2
Part I
Advanced Mechanical Design
December 2008
 Solar panels
 DC-DC buck converter
Solar power generation system
 Grid-tie inverter (GTI)
Objective
 stabilizing the inverter DC-link capacitor
 Omitting solar power oscillations
4
Solar power generation system

v out
controller
dynamics
C out v out
dv out
dt
 Ps  Pe
Synchronous Generator (SG)
5
SG dynamical equations
Inverter dynamical equations
  
  
 
1
M
 Pm
 Pe 
( Ps  Pe )
C out
x  x d
1  xd

 d
E q 
E
V cos(    )  E fd
q
T d 0  x d
x d
x q  x d

1  xq
d 


E d 
E
V
sin(



)

T q 0  x d
x d

1
 V R  K E E fd
E fd 
TE
1
 





 
E qr
 
E dr
(   ( v out 2  v outo 2 ) 2 )
 )
 x dr
( x  x dr

qr  dr
E
V cos(    )  E
 x

x
dr
dr

1
Td 0r
fdr
 )
( x qr  x dr

1  x qr


dr 
E
V
sin(



)



Tq 0 r  x dr
x dr


1
E fdr 
V Rr  K Er E fdr
T Er

 Inverter gain ( k in ) and ac voltage angle (  ) are the control inputs
6




Part II
Advanced Mechanical Design
December 2008
dc-dc buck converter control system
 Objective: Maintaining the solar power constant by adjusting duty cycle d
8
 Converter discrete-time equations
v in [( k  1)T ] 
i L [( k  1)T ] 
T
L
T
C in
[ iin [ kT ]  d i L [ kT ]]  v in [ kT ]
[ d v in [ kT ]  v out [ kT ]]  i L [ kT ]
 Photovoltaic array output current iin [kT ] is a nonlinear function of v in [kT ]
i in [ kT ]  n p I s  n p I o ( e
v in [ kT ] n s VT
1)
9
Part III
Advanced Mechanical Design
December 2008
v in [( k  1)T ] 
T
C in
T
[ iin [ kT ]  d i L [ kT ]]  v in [ kT ]
Input:
x1 [( k  1)T ]  f ( x [ kT ])  g ( x [ kT ]) u k
 Tracking error
:
T
x  [ x1 x 2 ]  [ v in i L ]
uk  d
z [ kT ]  x1 [ kT ]  x1d [ kT ]
z [( k  1)T ]  K z [ kT ]
0  K 1
stable
u  u d  K z [kT ]
u d   g ( x [ kT ])
1

f ( x [ kT ])  x1 d [( k  1)T ] 
11
u d   g ( x [ kT ])
1

f ( x [ kT ])  x 1 d [( k  1)T ]   W
T
 ( x , x 1 d [( k  1)T ])  
 : activation function
~
 Weight estimation error : Wˆ  W  W
 NN weight update law :
1
Wˆ [( k  1)T ]  c Wˆ [ kT ]  c  z [( k  1)T ]
c  1 : positive design constant
12
Part IV
Advanced Mechanical Design
December 2008
 System parameters
 AVR+PSS mechanism for inverter
 operational frequency of the converter : 10 kHz
 three-phase resistive load with R  6  on each phase
 Disturbance : load change from R  6  to R  5 . 3  at t  1 . 4 s
 solar module maximum power
:
Ps , mpp  1146
 solar module maximum power point voltage
:
W
v in , mpp  121 V
14
 Solar Voltage Less than MPP Voltage: v in , set  116 V
1140
120
Vin [V]
Ps [W]
1120
1100
1080
1060
With Controller
Without Controller
1
1.2
1.4
1.6
1.8
time [s]
2
2.2
2.4
115
110
105
With Controller
Without Controller
1
Converter input power
1.2
1.4
1.6
1.8
time [s]
2
2.2
2.4
Converter input voltage
 Disturbance between t=1.4s to t=1.6s
15
 Solar Voltage Less than MPP Voltage: v in , set  116 V
12
With Controller
Without Controller
105
IL [A]
100
With Controller
Without Controller
95
1.2
1.4
1.6
1.8
time [s]
2
2.2
11
10.5
2.4
10
1
1.2
Converter output voltage
1.4
1.6
1.8
time [s]
2
2.2
2.4
Converter inductance current
With Controller
Without Controller
9.9
Iin [A]
Vout [V]
11.5
9.8
9.7
9.6
1
1.2
1.4
1.6
1.8
time [s]
2
2.2
2.4
Converter input current
16
 Solar Voltage higher than MPP Voltage: v in , set  131 V
132
With Controller
Without Controller
Vin [V]
131
1050
1000
130
129
With Controller
Without Controller
128
1
1.2
1.4
1.6
1.8
time [s]
2
2.2
2.4
127
1
1.2
Converter input power
1.4
1.6
1.8
time [s]
2
2.2
2.4
Converter input voltage
100
98
Vout [V]
Ps [W]
1100
96
94
With Controller
Without Controller
92
1
1.2
1.4
1.6
1.8
time [s]
2
2.2
2.4
Converter output voltage
17
 Input Voltage Adjustment to Load Change:
R  5 .3
R  6
;
R  4 .6 
1 .8  t  2 .2 s ;
R  5 .3
0  t  1 .4 s
for
for
for
Vin [V]
1100
With Controller
Without Controller
1
1.5
2
time [s]
2 .2  t
2.5
3
115
110
105
With Controller
Without Controller
1
1.5
Converter input power
2
time [s]
2.5
3
Converter input voltage
110
105
Vout [V]
Pin [W]
1 .4  t  1 .8 s
120
1150
1050
for
100
95
90
With Controller
Without Controller
1
1.5
2
time [s]
2.5
Converter output voltage
3
18





The inverter is controlled by a novel stabilizer similar to power system stabilizer
(PSS).
The interaction of the solar array dc-dc converter with the GTI is addressed.
A nonlinear discrete-time model of a photovoltaic-connected buck converter was
presented.
Adaptive neural network (NN) controller is employed to enhance stability of dc-dc
converter connected to grid-tie inverter (GTI) in the presence of power system
disturbances.
Simulation results of the controller imply that the converter input voltage and power as
well as the inductor current are stabilized which verifies the accuracy of the converter
discrete-time model and the effectiveness of the proposed discrete-time controller.
19

Improve the efficiency and effectiveness of discrete-time adaptive neural network
in the power system stability and control

The system model can be developed to a more general distributed generation
system where other renewable generators or synchronous generators all are
interconnected. In this case each system is influenced by other subsystem’s states
and a more general control method is necessary.

The solar system connected dc-dc converter can be modeled in a dc distribution
system with interconnected subsystems working in high penetration of renewable
generation.
20
Thank You for Your Attention
21