Seminar_Jan_2010.pdf

Power Electronics in
Photovoltaic Applications
prof. Giorgio Spiazzi
Dept. of Information Engineering – DEI
University of Padova - ITALY
prof. Simone Buso
Dept. of Technology and Management of
Industrial Systems - DTG
University of Padova - ITALY

S. Buso, G. Spiazzi - Power Electronics in Photovoltaic Applications - CERN, January 2010 2
Summary
„ Photovoltaic module characteristics
„ Power converters for PV generators
„ Single stage topologies
„ Double or triple stage topologies
„ Control issues:
„ Maximum power point tracking
„ Anti-islanding techniques

Photovoltaic Effect
„ It is based on the generation of electron-hole pairs in a
semiconductor material illuminated by solar light.
„ A typical silicon photovoltaic cell generates an open
circuit voltage around 0.6-0.7 V with a short-circuit
current density in the order of 0.5-0.6 mA/mm2.
„ A photovoltaic module is composed by the series and/or
parallel connection of several photovoltaic cells (e.g. 36,
72)

„ I-V relation:
where:
php
phn
phD
ph I
I
I
I +
+
=
is the sum of the photo-generated currents in three
different semiconductor regions (p- and n-doped
regions as well as depletion region), and n is the
ideality factor (value between 1 and 2).
Mathematical Model of a Photovoltaic
Cell
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
= 1
e
I
I
I nkT
qV
o
ph
cell
cell

Mathematical Model of a Photovoltaic
Cell
„ The photo-generated current is a function of the
absorption coefficient, α(λ) [m-1], of the semiconductor
material and is given by an integral expression
representing the solution of the charge continuity
equation in a semiconductor region:
( ) ( )
( ) ( ) ( )( ) ( )( )
[ ]
∫
∫
+
−
+
−
−
−
−
−
−
=
=
λ
λ
α
λ
α
λ
λ
λ d
e
e
f
r
s
Aq
dx
)
x
(
G
Aq
I n
p
n
n
p
n
W
x
W
x
x
x
phD 1
1
where A is the exposed semiconductor area, s is the
fraction of it that is shaded by the metal contacts, r(λ) is
the surface reflectivity of the semiconductor material
and f(λ) is the photon flux (per unit area and unit
wavelength [s-1m-3]).

Equivalent Electrical Model
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
= 1
e
I
I
I nkT
qV
o
ph
cell
cell
vcell
+
Iph
icell
-
D
„ The I-V relation:
suggests a simple equivalent electrical model of the
PV cell:

„ Dissipative phenomena:
„ Non negligible resistivity of quasi-neutral regions as well as
of metal contacts (modeled with a series resistance in the
range 2-20 mΩ);
„ Internal recombination of photo-generated hole-electron
pairs (modeled with a shunt resistance in the range 0.5-5
Ω). This effect is often neglected!
Rsc
Rpc
vcell
+
Iph
icell
-
D

„ The I-V relation becomes:
Rsc
Rpc
vcell
+
Iph
icell
-
D
( )
pc
cell
sc
cell
nkT
I
R
V
q
o
ph
cell
R
I
R
V
1
e
I
I
I
cell
sc
cell
+
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
=
+

I-V Characteristics
Icell
Vcell
Iph
VOC
0
Icell
Vcell
Rs
VOC
ISC
0

I-V Characteristics
„ Fundamental parameters:
„ Short circuit current ISC (function of the luminous flux);
„ Open circuit voltage VOC (depends mainly on temperature);
ph
pc
SC
sp
nkT
I
qR
o
ph
0
V
cell
SC I
R
I
R
1
e
I
I
I
I
SC
sc
cell
≈
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
=
=
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ +
≈
=
= o
o
ph
0
I
cell
OC
I
I
I
ln
q
kT
V
V
cell

I-V Characteristics
„ Fundamental parameters:
„ Fill factor;
„ Conversion efficiency (R = radiation, W/m2, A = area, m2);
1
I
V
I
V
FF
SC
OC
MPP
MPP
<
=
A
R
PMPP
⋅
=
η
0
0
IMPP
VMPP VOC
PMPP
vP
iP

Photovoltaic Module
„ A photovoltaic module is, in general, composed by the
series connection of N cells (Rs = Ncells·Rsc, and
Rsh = Ncells·Rpc):
∑
=
=
cells
N
1
i
cell
P V
V
cell
P I
I =
}
Ncells
vp
+
Iph
-
ip
Rsh
Rs

Shadowing
0 Va,b
Va1
Vb1
IP1
IP2
Va2
IP
Regione
di
breakdown
ISCa
ISCb
VP
+
Ipha
IP
-
D
Iphb
D
+
-
Va
+
-
Vb
„ Ipha ≠ Iphb
„ At operating point P2, cell a behaves as a dissipative load

Shadowing: Using Bypass Diodes
„ Ipha ≠ Iphb
0 Va,b,P
Va1
Vb1 VP1
IP
IP2
ISCa
ISCb
IP1
Va2
Dbp
Dbp
VP
+
Ipha
IP
-
D
Iphb
D

Multiple Maxima
0 VP
PP
PMPP1
PMPP2
VMPP2
VMPP1
„ Power to voltage characteristic: multiple maxima

H245 modules (Helios
Technology):
38 or 72 cells
Voc = 20.5 V
Isc = 1.2-2.5 A
Dimensions:
524 mm x 325 mm
690 mm x 430 mm
800 mm x 430 mm
Example of Commercial Photovoltaic
Modules

Sharp 185 W modules:
72 cells series connected
Voc = 44.9 V
Isc = 5.75 A
Dimensions:
1575 mm x 826 mm
Modules

Sanyo HIP210 module
72 cells series connected
Voc = 50.9 V
Isc = 5.57 A
Dimensions: 1570 mm x 798 mm
Module
[A]
[V]
[A]
[V]

Example of Grid-Connected System
„ European Conversion Efficiency:
DC
DC
DC
AC
Inverter
CDC
vpv
-
+
vDC
-
+ LF +
vline
iline
PV
%
100
%
50
%
30
%
20
%
10
%
5
EU
2
.
0
48
.
0
1
.
0
13
.
0
06
.
0
03
.
0
η
+
η
+
η
+
η
+
η
+
η
=
η
hX% = conversion efficiency measured at P = X%·Pnom

Single-Phase Grid Connection
„ The power delivered to the grid has a dc value plus a
sinusoidal term at twice the line frequency
DC
AC
CDC
vDC
-
+ LF +
vline
iline
iDC
PL
pline(θ)
θ=ωlinet
0 π
( ) ( ) t
,
sin
V
2
v line
L
line ω
=
θ
θ
=
θ ( ) ( )
θ
=
θ sin
I
2
i L
line
( ) ( ) ( ) ( ) ( )
( )
θ
−
=
θ
=
θ
θ
=
θ 2
cos
1
I
V
sin
I
V
2
i
v
p L
L
2
L
L
line
line
line
„ Line voltage and current (unity power factor):

„ Hp: negligible energy processing at line frequency
DC
AC
CDC
vDC
-
+ LF +
vline
iline
iDC
DC
DC
line
L
DC
DC
line
DC
V
C
2
P
I
C
2
1
V
ω
=
Δ
ω
=
Δ
2
DC
V
line
L
2
DC
DC
DC
line
L
DC
V
r
2
P
V
V
V
2
P
C
DC
ω
=
Δ
ω
=
( ) ( ) ( ) ( )
( ) ( )
θ
−
=
θ
−
=
θ
⇒
θ
=
θ 2
cos
I
I
2
cos
1
V
P
i
p
p DC
DC
DC
L
DC
line
DC

„ Maximum allowed voltage ripple across DC link capacitor
(step-down inverter)
( ) ( )
θ
Δ
+
=
θ 2
sin
V
V
v DC
DC
DC
0 0.52 1.05 1.57 2.09 2.62 3.14
0
100
200
300
400
Vg(θ)
θ=ωlinet
VDC(θ)
θc
[V]
VD
C
ΔVDC
Example:
Vgpk = 390 V
VDC = 400 V
ΔVDC = 45.5 V

System Configuration
For domestic applications:

Example of Single-Stage Solutions
„ Step-down inverter with low-frequency
transformer
„ No DC current injection into the grid

Example of Single-Stage Solutions
„ Non isolated dual boost or dual buck-boost
„ Each converter generates a sinusoidal voltage (180° out
of phase) on top of a DC value that cancels across the
load
„ Capacitive filtering shared between Cs, C1 and C2

Dual-Stage Configurations
„ The DC-DC stage controls the PV string so as to operate at the
MPP and works under a constant output voltage VDC
„ The DC-AC inverter injects a sinusoidal current into the grid at a
unity power factor and controls the DC link voltage VDC
„ The DC link capacitor is located between the two converters (high
voltage means lower capacitor value)
DC
DC
DC
AC
CDC
vpv
-
+
vDC
-
+ LF +
vline
iline
PV
HF

MPP and generates a rectified sinusoidal voltage at its output
„ The maximum instantaneous power delivered by the DC-DC
stage is twice the average value
„ The DC-AC inverter operates at line frequency and unfolds the
rectified sinusoidal voltage into a sine wave
DC
DC
DC
AC
CDC
vpv
-
+
vrect
-
+ LF +
vline
iline
PV
LF

MPP and generates a rectified sinusoidal current at its output
„ The maximum instantaneous power delivered by the DC-DC stage
is twice the average value
„ The DC-AC inverter operates at line frequency and unfolds the
rectified sinusoidal current into a sine wave
DC
DC
DC
AC
LF
CDC
vpv
-
+ LF +
vline
iline
PV
irect

Example of Dual-Stage Solutions
„ Boost or flyback converter plus a PWM modulated
inverter

„ Push-pull converter plus a line-frequency commutated
inverter (Mastervolt Soladin 120 )

„ Boost converters plus a PWM modulated half-bridge
inverter (SMA SunnyBoy 5000TL )

„ Isolated boost converters plus a PWM modulated full-
bridge inverter (Powerlink PV 4.5kW )

Control Implementation
„ Double stage system configuration:
+
-
+
+
+
-
PLL
MPPT
dc
dc
dc
ac
PWM
PWM Gi
Gv
VDC,ref
VDC
D Ir
IrFF
Iref
sin(θ)
vg
VgRMS
εv
εi
ig
ig,ref
vpv
ipv
ppv
PV
array
AC Grid
gRMS
pv
V
p
2

Maximum Power Point Tracking
(MPPT)
„ The photovoltaic module maximum power point changes with time
and operating conditions, like illumination and temperature.
„ All modern photovoltaic systems include a switching converter
aimed to control the photovoltaic module operating point, i.e. that
implements a Maximum Power Point Tracking (MPPT) function.
„ The effectiveness of a MPPT technique is defined as the ratio
between the extracted power and the maximum available power,
i.e.:
MPP
P
MPPT
P
P
=
η

MPPT
0
0
IMPP
VMPP VOC
PMPP
vP
iP
0
dv
dp
p
p
> 0
dv
dp
p
p
<
„ ip-vp and pp-vp static characteristics

MPPT
„ P&O (Hill Climbing)

MPPT: P&O (Hill Climbing)
„ Easily implemented in digital form
(microcontroller).
„ Existence of limit cycle oscillations (LCO)
around the MPP
„ Constant or variable perturbation amplitude
(high perturbation amplitude means high
speed of response but lower effectiveness
due to limit cycle oscillations).

MPPT: Incremental Conductance
( )
MPP
MPP
P
P
MPP
MPP
P
P
P
P
MPP
P
P
P
MPP
P
P
I
dv
di
V
i
dv
di
v
dv
i
v
d
dv
dp
+
=
+
=
=
MPP
MPP
MPP
P
P
MPP
P
P
V
I
dv
di
0
dv
dp
−
=
⇒
=
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎨
⎧
−
>
−
<
−
=
MPP
of
eft
l
V
I
dv
di
MPP
of
ight
r
V
I
dv
di
MPP
at
V
I
dv
di
MPP
MPP
P
P
MPP
MPP
P
P
MPP
MPP
P
P

„ Easily implemented in digital form
(microcontroller).
„ Able, in theory, to reach the exact MPP. In
practice, due to quantization and limited
resolution, limit cycle oscillations exist.
„ Constant or variable perturbation amplitude
(high perturbation amplitude means high speed
of response but lower effectiveness due to limit
cycle oscillations).

MPPT: Ripple Correlation
„ Based on correlation between AC components of output
power and voltage (or current) of PV panel
( )
( )
∫ τ
=
t
0
p
d
dx
x
dp
k
t
x
where x stands for vP or iP

Weighting function
Weighting function
( )
( )
∫ τ
=
t
0
v d
dv
v
dp
k
t
v
( )
( ) ( )
∫
∫ τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
τ
=
τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
=
t
0
t
0
2
d
d
dv
d
v
dp
k
d
d
dv
dv
v
dp
k
t
v
( )
( )
∫ τ
=
t
0
i d
di
i
dp
k
t
i
„ The use of a positive weighting function allows to
consider time derivatives of variables

( )
( ) ( )
∫
∫ τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
τ
=
τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
τ
−
=
t
0
d
t
0
d d
d
di
d
i
dp
k
d
d
dv
d
v
dp
k
t
d
„ If a switching converter is used to process the PV power,
the duty-cycle can be used to control PV voltage or
current ….
( ) ∫
∫ τ
=
τ
−
=
t
0
d
t
0
d d
i
~
p
~
k
d
v
~
p
~
k
t
d
… and the power and voltage derivatives can be
substituted by switching ripple components

( ) ∫ =
τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
−
=
t
0
d d
d
dv
sign
d
dp
sign
k
t
d
( ) ( ) ( ) ( ) ( )
∫
∫ τ
=
τ
−
=
t
0
d
t
0
d d
i
~
sign
p
~
sign
k
d
v
~
sign
p
~
sign
k
t
d
„ Alternative approach: only sign information can be used
∫ τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
⎟
⎠
⎞
⎜
⎝
⎛
τ
=
t
0
d d
d
di
sign
d
dp
sign
k

MPPT: Current Sweep
„ Based on periodical measurement of ip-vp characteristic
through a current sweep
„ Some loss of effectiveness due to the measurement
process
( ) ( )
( )
dt
t
df
k
t
f
t
iP =
=
( )
( )
( )
( )
( )
0
dt
t
dv
t
f
dt
t
df
t
v
dt
t
dp P
P
P
=
+
=
( )
( )
( ) ( )
0
dt
t
df
dt
t
dv
k
t
v
dt
t
dp P
P
P
=
⎟
⎠
⎞
⎜
⎝
⎛ +
= ( )
( )
0
dt
t
dv
k
t
v P
P =
+
( ) ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
= τ
−
t
SCe
I
t
f

MPPT: Current Sweep
f(t)
generator
(to dc-dc
controller)
Hold VMPP
vp ( ) τ
−
=
t
SC
P e
I
t
i
( )
( )
dt
t
dv
t
v P
P τ
− +
-
+
-
ip
Timing
unit dc-dc converter
disable signal

„ Islanding: a continuous operation of an inverter
(or other generator) connected to the utility grid
when the latter is disconnected.
Anti-islanding
To be avoided because:
„ It can be harmful to people (particularly for the
grid management personnel).
„ It can cause malfunctions and/or failures of
connected loads due to voltage parameters out
of range (RMS value, frequency, etc.).

„ Load matching: the active and reactive power
generated by the inverter should match the load needs
(active and reactive power delivered by the grid should
be zero just before disconnection)
Anti-islanding
Conditions for islanding detection tests:
ΔP=0, ΔQ=0
PV array
vp
+
ip
{
-
DC
AC
+
vline
L C R
S1
P,Q
Inverter
+
-
V
Load represented
by parallel R-L-C

„ In practice, it is not strictly necessary for the active and
reactive power coming from the utility grid to be zero
„ Anti-islanding methods differ in the amplitude and
shape of the Non detection Zone (NDF) in the ΔP-ΔQ
plane
Anti-islanding
ΔP=0, ΔQ=0
PV array
vp
+
ip
{
-
DC
AC
+
vline
L C R
S1
P,Q
Inverter
+
-
V
Load represented
by parallel R-L-C

„ Passive Methods: some grid parameters (voltage
amplitude, frequency, etc.) are monitored at the Point of
Common Coupling (PCC) (no degradation of power
quality, but poor effectiveness)
„ Active Methods: perturbations are introduced so as to
detect the presence of the utility grid (some degradation
of power quality is expected)
„ Methods taken by the utility grid manager
(measurements, communications, etc.)
Anti-islanding Methods

„ Assuming a unity power factor inverter, i.e. Q = 0, if before
disconnection ΔP ≠ 0, the RMS voltage at PCC will vary, thus
triggering the Over/Under Voltage protection circuitry
„ Assuming a unity power factor inverter, i.e. Q = 0, if before
disconnection ΔQ ≠ 0, the current-to-voltage phase shift induced
by the load will force the inverter to move the frequency toward the
load resonant value so as to achieve Q = 0, thus triggering the
Over/Under Frequency protection circuitry
Passive Methods: OUV - OUF
PV array
vp
+
ip
{
-
DC
AC
+
vline
L+ΔL
C+ΔC
R+ΔR
S1
P,Q
Inverter
ΔP≠0, ΔQ≠0
+
-
V

„ Pros:
„ Low cost
„ Easy to implement
„ Cons:
„ Wide Non
Detection Zone
Passive Methods: OUV - OUF
PV array
vp
+
ip
{
-
DC
AC
+
vline
L+ΔL
C+ΔC
R+ΔR
S1
P,Q
Inverter
ΔP≠0, ΔQ≠0
+
-
V

„ Pros:
„ Cons:
„ Difficult to select
the threshold
Passive Methods: Phase Jump
Detection
„ For current-controlled inverters: the internal PLL synchronize the
current with the voltage zero crossing. When the island is formed, the
voltage at PCC undergoes a jump (due to the reactive nature of the
load) that will lead to a different zero crossing that can be detected

„ Pros:
„ Cons:
„ Affected by the line impedance
„ Difficult to select the threshold
„ Effectiveness reduction due to loads with
low-pass characteristics
Passive Methods: Harmonic Detection
„ It is based on the measurement of the Total Harmonic Distortion of
the voltage at PCC (in the presence of the grid, the current
harmonics produced by non linear loads and the inverter itself are
bypassed by the small line impedance)

Active Methods: Active Frequency Drift
„ A current-controlled inverter forces a frequency shift in the
output current: in the presence of the grid, the line
frequency zero crossing of the voltage at PCC reset the
process
t
Tv/2
Ti/2
io(t) io_ideale(t)
tz
t
Tv/2
Ti/2
io(t)
io_ideale(t)
tz

„ Pros:
„ Easy to implement in a microprocessor
„ Cons:
„ Increase of current harmonic distortion
„ Affected by the presence of other inverters
connected to the same PCC
Active Methods: Active Frequency Drift
„ A current-controlled inverter forces a frequency shift in the
output current: in the presence of the grid, the line
frequency zero crossing of the voltage at PCC reset the
process

Active Methods: Sandia Frequency
Shift
„ It is based on a positive feedback on the frequency of the
voltage at PCC
Chopping fraction:
v
z
T
t
2
cf =
t
Tv/2
Ti/2
io(t) io_ideale(t)
tz
( )
n
0 f
f
K
cf
cf −
+
=
cf0 = chopping fraction at zero
frequency error
fn = nominal frequency
K = gain

Active Methods: Sandia Frequency
Shift
„ It is based on a positive feedback on the frequency of the
voltage at PCC
„ Pros:
„ Good trade-off between effectiveness and power
quality
„ Cons:
„ Slight degradation of power quality
„ NDZ caused by high Q resonant loads

Active Methods: Sandia Voltage Shift
„ It is based on a positive feedback on the RMS value of
the voltage at PCC: if the voltage increases the inverter
increases the injected current (i.e. the power), and
viceversa. If the grid is connected, the power variation is
absorbed by the grid itself.
„ Pros:
„ Cons:
„ Slight degradation of power quality
„ Slight degradation of system effectiveness because the
variation of the inverter output power moves the PV
operating point out of MPP

Anti-Islanding Methods
„ No one of the proposed anti-islanding
methods can be considered satisfactory in
terms of Non Detection Zone and/or dynamic
response
„ The best approach could be to implement two
or more different methods so as to minimize
the probability of false triggering and/or lack
of intervention

Thank you for your attention!

Seminar_Jan_2010.pdf

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