Power Electronics and Control in
Grid-Connected PV Systems
ECEN 2060
Grid-Connected PV System
One possible grid-connected PV system architecture
IPV
DC input
VPV , I PV
PPV = VPV I PV
iac
+
PV
array
VPV
−
AC output
+
Power
electronics
converter
vac
−
AC
utility
grid
v ac (t ) = 2VRMS sin (ωt )
iac (t ) = 2 I RMS sin (ωt )
Pac = VRMS I RMS
pac (t ) = vac iac = VRMS I RMS (1 − cos(2ωt ))
Functions of the power electronics converter
• Operate PV array at the maximum power point (MPP) under all conditions
• Generate AC output current in phase with the AC utility grid voltage
• Achieve power conversion efficiency close to 100%
P
V
I
η converter = ac = RMS RMS
PPV
VPV I PV
• Provide energy storage to balance the difference between PPV and pac(t)
Desirable features
• Minimum weight, size, cost
• High reliability
ECEN2060
2
Power Electronics for Grid-Connected PV System
One possible realization:
Energy-storage
capacitor
IPV
+
PV
array
VPV
iac
+
+
Boost
DC-DC
converter
C
VDC
−
Single-phase
DC-AC
inverter
−
−
DC-DC control
vac
AC
utility
grid
DC-AC control
Boost DC-DC converter
•
Set the PV operating point (VPV, IPV) to MPP
•
Efficiently step up VPV to a higher DC voltage VDC
DC-AC inverter
•
Efficiently generate AC output current iac in phase with the AC grid voltage vac
• Balance the average power delivery from the PV array to the grid, Pac = Ppv * ηDC-DC * ηDC-AC
Energy storage capacitor C
•
Balance the difference between the instantaneous power pac(t) and the average power
The system must be disconnected from the grid if the utility loses power
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DC-AC Inverter Control
One possible realization:
Energy-storage
capacitor
IPV
+
PV
array
VPV
iac
+
+
Boost
DC-DC
converter
C
−
VDC
Single-phase
DC-AC
inverter
−
−
DC-DC control
vac
AC
utility
grid
DC-AC control
= IRMSref
• The control variable for the DC-AC inverter is the RMS current reference IRMSref
• The inverter output current iac(t) is controlled so that it is in phase with the grid voltage vac(t)
and so that it’s RMS value equals the reference:
IRMS = IRMSref
One possible current control approach, based on a comparator with hysteresis, has been
discussed in class, see Intro to Power Electronics notes
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Simulation model: pv_boost_dcac_averaged.mdl
ECEN2060
6-module PV Array
Ipv
1000
PV module (I)
Insolation
Vout (boost) = VDC
Ppv
Ipv
PV module (I)
Insolation
Boost
Vpv
PV1
Insolation
Vg
Vpv
Ppv
Vout
DC-DC
(averaged, C)
current control D
Set Boost Iref to
operate PV array
at MPP
Iout
4.95
Iref
ef f iciency
PV module (I)
Ipv = Iref
PV current
Vpv
Duty
Boost scope
ef f iciency
Vpv
Vpv
Ppv
PV module (I)
Insolation
(averaged)
D
pin
PV module (I)
Insolation
3.94
Boost efficiency
iin
Duty
pin
pin, pout
pout
Iref
Set DC-AC Iref
to balance
the power, i,e
to keep VDC
constant
IRMSref
Average output AC power
1
s
Vpv
510.8
Ppv
Integrator(pout)
103.2
Vpv
Vpv
Integrator(pin)
Pout
fac_out
DC-AC average power
and efficiency
1
s
472.8
60
Ppv
PV5
PV module (I)
iac
DC-AC Inverter
Pout boost
Boost DC-DC
Ppv
PV output power
Ipv
iin
v ac
Vpv
PV4
Ipv
inverter
pout
Product
Ipv
iac
492.6
Pout
Ppv
PV3
DC-AC
Iref
0.9643
Insolation
v ac
Vdc
Vout
PV2
Ipv
DC-AC
scope
199.8
Vpv
60
fac_in
0.9586
Compute
efficiency
DC-AC Efficiency
493.2
Pin
Average input AC power
Insolation
Ppv
PV6
Add
ECEN2060
PV + Boost DC-DC + DC-AC inverter averaged model
Ipv = Iref
ECEN2060
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How to achieve average power balance?
Simulation example:
• 6-module (85 W each) PV array with full sun (1,000 W/m2 insolation)
• PV array operates at MPP: Ppv = 6*85 W = 510 W
• AC grid RMS voltage: 120 V
• Run simulations for 3 different values of IRMSref and observe boost output voltage Vout(t) = VDC(t)
IRMSref = 3.4 A
IRMSref is too low
Pac < Ppv
VDC increases
IRMSref = 4.4 A
IRMSref is too high
Pac > Ppv
VDC decreases
IRMSref = 3.94 A
IRMSref is just right
Pac ≈ Ppv
VDC starts at 200 V
and returns to 200 V
ECEN2060
Tac = AC line period (1/60 seconds)
6
Average Power Balance by Automatic Feedback Control
IPV
iac
+
+
PV
array
VPV
Boost
DC-DC
converter
+
Single-phase
DC-AC
inverter
VDC
−
−
DC-DC control
vac
AC
utility
grid
−
+
IRMSref
−
VDCref
compensator
• Voltage VDC is sensed and compared to a reference value VDCref (e.g. VDCref = 200 V)
• The difference VDC – VDCref is the error signal for the feedback controller
• If the error is positive, i.e. if VDC is greater than VDCref, the compensator increses IRMSref
• If the error is negative, i.e. if VDC is less than VDCref, the compensator decreases IRMSref
• In steady-state, IRMSref adjusted by the automatic feedback controller is just right so that
VDC = VDCref, error signal is zero, and the average power Pac delivered to the AC grid
matches the power generated by the PV array
• Stability, dynamic responses and realizations of feedback controllers are topics beyond the
scope of this class. These topics are addressed in Circuits, and more advanced Control
and Power Electronics courses
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Energy storage
Energy-storage
capacitor
IPV
+
PV
array
VPV
iac
+
+
Boost
DC-DC
converter
Pac pac(t)
C
−
VDC
Single-phase
DC-AC
inverter
−
−
DC-DC control
vac
AC
utility
grid
DC-AC control
Pac − p ac (t ) = Pac − Pac (1 − cos 2ωt ) = Pac cos 2ωt
Pac > pac(t), capacitor C is charged up
∆vDC
Pac < pac(t), capacitor C is discarged
• Capacitor C provides energy storage necessary to balance instantaneous power delivered to the grid
• Magnitude of the resulting voltage ripple ∆VDC at twice the line frequency (2 x 60 = 120 Hz) depends
on the average power Pac and capacitance C
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Energy storage capacitor C
Pac − pac (t ) = Pac − Pac (1 − cos 2ωt ) = Pac cos 2ωt
Pac > pac(t), capacitor C is charged up
∆vDC
Pac < pac(t), capacitor C is discarged
• Energy supplied to the capacitor during the time when Pac > pac(t), i.e. when the capacitor
is charged from VDCmin to VDCmax
Tac / 8
π /2
ac
−π / 2
P
∆EC = ∫ Pac cos 2ωt dt = ac
2ω
−T / 8
∫ cosθ dθ =
Pac
ω
• This energy must match the change in energy stored on the capacitor:
∆E C =
VDC max + VDC min
1
1
2
2
CV DC
−
CV
=
C
(
V
−
V
)
≈ CVDC ∆VDC
max
DC min
DC max
DC min
2
2
2
• Solve for the ripple voltage:
CV DC ∆VDC =
ECEN2060
Pac
ω
∆VDC =
Pac
CV DC ω
9
Energy storage analysis example
• DC-AC inverter input voltage: VDC = 200 V
• Average power delivered to the grid: Pac = 600 W
• Find C so that ∆VDC = 40 V (i.e. +/-10% of the DC voltage at the input of the DC-AC inverter)
• Solution:
CV DC ∆VDC =
C=
Pac
ω
Pac
600 W
=
= 200 µF
∆VDCVDC ω 40 V * 200 V * 2π 60 Hz
• Note that the energy supplied (or absorbed) by the capacitor is relatively small:
∆EC =
Pac
ω
=
600
= 1.6 J
2π 60
• The total energy stored on the capacitor is also small
EC =
1
2
CVDC
= 4J
2
• This example illustrates the need for only relatively small energy storage in a gridconnected system, easily accomplished by a capacitor, in sharp contrast to stand-alone
PV systems that require very significant energy storage (e.g. batteries)
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Maximum Power Point (MPP) Tracking
Energy-storage
capacitor
IPV
+
PV
array
VPV
iac
+
+
Boost
DC-DC
converter
−
C
Single-phase
DC-AC
inverter
VDC
−
−
DC-DC control
vac
AC
utility
grid
DC-AC control
Choices for the Boost DC-DC control variable:
• Duty cycle D
• Input current reference Iref
• Input voltage reference Vref
• The objective of the MPP tracking algorithm is to adjust the DC-DC control
variable so that the PV array operates at the maximum power point
• In the example discussed here:
• It is assumed that the Boost output voltage Vout = VDC is constant
• Iref is used as the control variable for the Boost DC-DC converter
• PV array current ideally tracks the Boost input current reference: IPV = Iref
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Reminder: PV array characteristic
• Example: six 85 W modules in series, full sun
Ipv [A]
6
5
4
3
2
1
0
ECEN2060
0
20
40
60
80
100
120
Vpv [V]
12
Ppv as a function of Vpv
• Example: six 85 W modules in series, full sun
Ppv [W]
500
450
400
350
300
250
200
150
100
50
0
0
ECEN2060
20
40
60
80
100
120
Vpv [V]
13
Ppv as a function of Ipv = Iref
• Example: six 85 W modules in series, full sun
MPP
Ppv [W]
500
450
400
350
300
250
200
150
100
50
0
0
1
2
3
4
5
6
Ipv = Iref [A]
Objective: adjust Ipv = Iref to operate at MPP
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Simple “perturb and observe” MPP tracking algorithm
MPP
Initialize Iref, ∆Iref, Pold
500
450
Ppv
400
350
Measure Ppv
300
250
200
YES
150
Ppv > Pold ?
100
50
0
0
NO
1
2
3
4
5
6
Ipv = Iref
Always step Iref in the
direction of increasing Ppv
Change
direction
Continue
in the
same
direction
∆Iref = −∆Iref
Iref = Iref +∆Iref
Pold = Ppv
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MATLAB code: MPP tracking algorithm initialization
Initialize Iref, ∆Iref, Pold
Measure Ppv
YES
NO
Ppv > Pold ?
Change
direction
Continue
in the
same
direction
∆Iref = −∆Iref
Iref = Iref +∆Iref
Pold = Ppv
ECEN2060
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MATLAB code: MPP tracking algorithm
Initialize Iref, ∆Iref, Pold
Measure Ppv
YES
NO
Ppv > Pold ?
Change
direction
Continue
in the
same
direction
∆Iref = −∆Iref
Iref = Iref +∆Iref
Pold = Ppv
ECEN2060
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Simulation model: pv_boost_mpp_Iref.mdl
Insolation 1-5
Ipv
S1
(time varying)
1000
S1-5
(constant)
ECEN2060
6-module PV Array
85 x 6 = 510 W DC system
PV module (I)
Insolation
Select
insolation
for modules
1-5
103.4
Vpv
1 time unit = 1 minute
Vpv
Ppv
0.9644
4.94
PV1
Ipv
ECEN 2060 PV array with
MPP tracking
Boost DC-DC converter
PV voltage
PV module (I)
Insolation
200
Ipv
Vout
Vout
Vpv
Vpv
Vpv
Iout
Boost
DC-DC
(averaged)
Pout
Iref control
Boost efficiency
Pout
Vg
ef f iciency
ef f iciency
Ppv
Iref
PV2
D
Duty
Boost DC-DC
Ipv
PV module (I)
Insolation
Ppv
PV3
Vpv
Ppv
Ipv
PV module (I)
Insolation
P
MPPT Iref
Vpv
Iref 1
4
Select
controller
Iref
(constant)
Insolation
PV MPP
scope
Iref
Ppv
PV module (I)
Vpv
PV power
Ppv
510.8
PV5
Insolation 6
Iref
Compute
Ppv
PV4
Ipv
Vpv
MPP tracking
controller
MPPtrackIref.m
Vpv
Ppv
PV energy [kWh]
Ipv
S6
(time varying)
1000
S6 (constant)
PV module (I)
Insolation
1
s
Vpv
Ppv
PV6
Select
insolation
for
module 6
Ipv
Integrate
Ppv
Add
1
Ppv
Pout, Ppv , Pideal
Ppv
ideal
5
1
Epv
kWh (pv)
Iref
Ipv = Iref
5 modules
4.081
-K-
Ideal PV energy [kWh]
-K85/1000
Ppv
ideal
1
s
Integrate
Pideal
-KConvert to
kWh
4.087
Eideal
Integrate
Pout
1
s
kWh (out)
-K-
Output energy [kWh]
3.936
Eout
1 module
ECEN2060
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MPP tracking operation
Boost DC-DC converter duty cycle D
PV array voltage Vpv
Boost DC-DC converter input current reference, Iref = Ipv
PV array output power Ppv compared to ideal Ppv @ MPP
ECEN2060
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The Future of
Grid-Connected PV Systems
Ipv, Vpv
Ipv, Vpv
PV
Converter
PV
Converter
Ipv, Vpv
Controller
Ipv, Vpv
Controller
Ipv, Vpv
Ipv, Vpv
Converter
PV
Converter
PV
Inverter
Ipv, Vpv
Controller
Ipv, Vpv
Ipv, Vpv
60 Hz AC
Utility
Controller
Ipv, Vpv
PV
Converter
PV
Converter
Ipv, Vpv
Controller
Ipv, Vpv
Controller
Innovations in system
architecture, control,
and power electronics
circuit design
• Scalable modular power electronics: distributed DC-DC conversion
• Much improved performance in the presence of module mismatches or partial shading
• Ongoing projects in the Colorado Power Electronics Lab (CoPEC) at CU ECE Dept led
by Prof. Erickson
ECEN2060
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Module-Integrated DC-DC Converter (MIC)
for the Smart PV Roofs
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