On Extending the Energy Balancing Limit of
Multilevel Cascaded H-Bridge Converters for Largescale Photovoltaic Farms
© 2013 IEEE
Australasian Universities Power Engineering Conference (AUPEC), 29 Sept. – 3 Oct 2013, Hobart, Tasmania,
On Extending the Energy Balancing Limit of Multilevel Cascaded H-Bridge
Converters for Large-scale Photovoltaic Farms
Yifan Yu
Georgios Konstantinou
Branislav Hredzak
Vassilios G. Agelidis
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Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, TAS, Australia, 29 September – 3 October 2013
1
On Extending the Energy Balancing Limit of
Multilevel Cascaded H-Bridge Converters for
Large-scale Photovoltaic Farms
Yifan Yu
Georgios Konstantinou
Branislav Hredzak
and
Vassilios G. Agelidis
Australian Energy Research Institute and School of Electrical Engineering and Telecommunications,
The University of New South Wales, Sydney, NSW, 2052, Australia
email: yifan.yu@student.unsw.edu.au
g.konstantinou@unsw.edu.au
b.hredzak@unsw.edu.au
vassilios.agelidis@unsw.edu.au
Abstract—When multilevel cascaded H-bridge converters are
used to interface large-scale photovoltaic farms to the electricity
grid, the stochastic variation of irradiance and other factors
lead to unequal power generation among the phases, affecting
the three-phase balanced system. Injections of fundamental
frequency zero sequence to modulation references can deal with
this problem. This paper proposes the third harmonic injection
to extend the balancing limit of three-phase unbalanced power
generation. The concepts and definitions of converter energy
balancing limit are presented to assess its energy balancing
capability. Numerical comparison results reveal that the proposed
third harmonic injection method has greater energy balancing
capability. Selected simulation results are provided to verify the
performance of the proposed method.
Index Terms—AC-DC power converters; Photovoltaic systems
Lf
Phase A
ia
H-Bridge A1
PV String Isolated DC-DC Converter
Idc
ib
ic
H-Bridge
Ipv
Vc
Vpv
H-Bridge A2
I. I NTRODUCTION
In the next few decades, photovoltaic (PV) power generation
is expected to gain much higher energy market share, due to
the ever-decreasing costs of PV panels and their associated
power conditioners [1], [2]. The majority of the contemporary commercially available PV converters are designed for
small or medium-scale residential PV generators up to several
hundred kilo-watts [3], [4]. Large-scale mega-watt (MW) PV
farms, nevertheless, are more economically attractive due
to their reduced cost per watt, higher conversion efficiency,
reduced intermittency and ultimately to their control as a
conventional power station.
The PV industry is not alone in the pursuit of high power
converters. The electric motor drives industry also suffered
in the 1980s and then conquered this barrier through the
widespread application of multilevel converters [5]–[7]. By
synthesizing voltage waveforms with multiple levels, this technology allows converters to withstand higher voltage with low
voltage rating devices. Furthermore, the multilevel waveform
decreases the average switching frequency of the devices,
and, hence, the converter switching losses. Duplicating the
technical success of multilevel converters in the emerging
renewable energy industry has been an interesting topic for researchers worldwide [8]–[12]. However, several barriers have
to be conquered on its way to the ultimate industrial success,
H-Bridge A3
Phase B
Phase C
n
Fig. 1. Three-phase seven-level cascaded H-bridge converter.
due to some unique requirements of the PV generators, such as
Maximum Power Point Tracking (MPPT) and intermittency.
Compared to other multilevel converter topologies such as
the Neutral Point Clamped (NPC), Flying Capacitor (FC) and
Modular Multilevel Converter (MMC), the Cascaded H-Bridge
(CHB) has been accepted as the most suitable candidate for
the next generation PV farm converters [13], due to multiple
separate low voltage DC links. These are considered a major
drawback for industrial drives but are now a perfect match to
PV systems. A three-phase seven-level CHB converter consists
of nine H-bridges, each fed by multiple strings of PV panels
via their own isolated DC-DC converters as shown in Fig. 1. In
this way, the capacitor voltages are regulated by the grid via Hbridges, while each DC-DC converter does independent MPPT
to maximize the captured PV power. The merits of separate
DC links and the proven multi-string configuration are fully
deployed to achieve better efficiency and higher power ratings.
One problem that needs to be addressed with CHB is the
Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, TAS, Australia, 29 September – 3 October 2013
unbalanced power generation by the PV panels connected
to each H-Bridge, due to unequal radiation, temperature and
panel parameters. It should be noted that balanced three-phase
grid injection currents are required by the grid code [14].
As a consequence, control methods need to be modified in
order to deliver balanced three-phase currents to the grid, even
under unequal power generation from each phase. In [12], a
continuous time domain energy balancing control algorithm
was presented to solve inter-bridge unbalance for the singlephase seven-level CHB converter. However, due to the absence
of interfacing DC-DC converters, the capacitor voltage of the
individual H-bridge has to be variable to achieve local MPPT,
resulting in undesirable harmonic spectrum. Moreover, the
lack of galvanic isolation limits the operational DC voltage to
1000V due to safety considerations, thus making it less attractive for large-scale applications. A fundamental frequency zero
sequence, which was firstly presented for capacitor voltage
balancing of CHB based Static Synchronous Compensator
(STATCOM) [15], was later deployed to redistribute the generated power among the three phases of the CHB PV converter
[16]. Another zero sequence, the min-max sequence [17],
was also proposed for the same purpose, which features very
simple calculation but results in sub-optimal energy balancing
control.
Although it has been confirmed that these energy balancing
control methods can achieve rebalancing with an extra zero
sequence injection for some demonstrated cases, the energy
balancing limit, i.e. the limit to which three-phase balanced
currents are maintained despite of the different amount of
power generated by each PV module, has not been addressed.
The objective of this paper is firstly to investigate analytically
the energy balancing limit of existing methods and secondly
to report a more advanced zero sequence injection method
aiming to increase such limit.
The rest of the paper is organized as follows. In Section II, the fundamental frequency zero sequence injection
to redistribute the power among the phases is calculated
based on the phasor diagram. The fundamental concepts and
definitions of energy balancing limit are presented in Section
III. A third harmonic injection method that maximizes the
converter energy balancing limit is proposed in Section IV,
followed by the energy balancing limit comparison between
the existing and proposed methods in Section V. Section VI
provides computer simulations based on MATLAB/PLECS to
verify the performance of the proposed approach. Finally, the
conclusions are summarized in Section VII.
II. P OWER R EDISTRIBUTION BY F UNDAMENTAL
F REQUENCY Z ERO S EQUENCE I NJECTION
In the balanced operation of a CHB converter, equal amount
of power is generated by each phase and the respective threephase voltages and currents are displaced by 120 degrees
having the same amplitude, as demonstrated in Fig. 2a. Vga ,
Vgb , Vgc and Iga , Igb , Igc represent the grid voltage and
current vectors, respectively, and Vca , Vcb , Vcc are the
jωLfIgc
C
Vgc
Sector II
Vcc
Sector III
2
Sector I
Igc
Vca
jωLfIga
A
α
n
Iga
Vga
Igb
Sector VI
Sector IV
Vcb
Vgb
B
jωLfIgb
Sector V
(a)
C
Vgc
Vcc
Sector II
Sector I
Sector III
Igc
Vca
n' V0
θ
ω
Iga
Vga
A
Igb
Sector IV
Vgb
B
Vcb
Sector VI
Sector V
(b)
Fig. 2. Phasor diagram of (a) balanced operation (b) unbalanced operation
with fundamental frequency zero sequence injection.
fundamental frequency vectors of the converter output phase
voltage.
When the power generated by the PV modules connected
to different phases is unequal, due to partial shading or other
reasons, the situation becomes complicated. The three-phase
grid currents will be asymmetrical if the converter phase
legs are still modulated with the same reference waveform.
Injection of a fundamental frequency zero sequence is one
way to solve this problem [16]. As depicted in Fig. 2b, the
injected zero sequence does not alter the line-to-line voltages
seen by the grid, which makes it possible to deliver threephase balanced currents to the grid even under unbalanced
power generation. Additionally, it generates different amount
of power with the grid current of each phase, but zero net
power when considering the three phases as a whole. Therefore, the zero sequence redistributes the power among three
Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, TAS, Australia, 29 September – 3 October 2013
phases as required to provide three-phase balanced currents.
With the introduction of this fundamental frequency zero
sequence, the three-phase voltage references can be rewritten
as follows:
√
√
Vca = 2Vcp cos(ωt + α) + 2V0 cos(ωt + θ),
(1)
Vcb =
Vcc =
√
2Vcp cos(ωt + α − 120◦ ) +
√
◦
2Vcp cos(ωt + α + 120 ) +
√
P(A,B,C)
,
Ppeak /3
(4)
where Ppeak refers to the rated peak power of all PV modules
connected to the converter. The location of zero sequence
based on the three-phase power generation is summarized in
Table I.
The case of zero sequence vector located in Sector I is
analyzed in detail before a more generalized relationship
is developed. According to the phasor diagram depicted in
Fig. 2b, the power redistribution caused by the injected zero
sequence for each phase can be expressed as:
!
λA + λB + λC Ppeak
V0 Ig cos θ = λA −
,
(5)
3
3
!
λA + λB + λC Ppeak
V0 Ig cos(θ + 2π/3) = λB −
, (6)
3
3
!
λA + λB + λC Ppeak
V0 Ig cos(θ − 2π/3) = λC −
, (7)
3
3
√
Three-phase Power Ratio
2V0 cos(ωt + θ), (3)
where Vcp and α are the rms value and phase angle of the
positive sequence of Phase A, and V0 and θ represent the rms
value and phase angle of the injected zero sequence vector.
As illustrated in the phasor diagram of Fig. 2b, the addition
of the fundamental frequency zero sequence vector only shifts
the fictitious neutral point with the line-to-line voltage seen
from the grid unchanged.
The location of the zero sequence generation depends on the
actual power generation of each phase and can be located in
and of the six sectors (I-VI). Here, λA , λB , λC are defined as
the power generation ratios, which are computed by comparing
the actual power of each phase to its rated peak power:
λ(A,B,C) =
TABLE I
L OCATION OF Z ERO S EQUENCE V ECTOR BASED ON T HREE - PHASE
P OWER G ENERATION
2V0 cos(ωt + θ), (2)
√
λA + λB + λC
3Vg Ig =
Ppeak ,
(8)
3
where Vg and Ig stand for the rms value of grid voltage and
current. The amplitude of the zero sequence vector and its
phase displacement can then be calculated as:
√
6∆
V0 =
Vg ,
(9)
3(λA + λB + λC )
!
√
6(λC − λB )
θ = arcsin
,
(10)
2∆
3
Sector
λB < λ C < λ A
I
λB < λ A < λ C
II
λA < λ B < λ C
III
λA < λ C < λ B
IV
λC < λ A < λ B
V
λC < λ B < λ A
VI
where:q
2
2
2
∆ = (λA − λB ) + (λB − λC ) + (λA − λC ) .
(11)
After performing similar analysis in other sectors, it is found
that the representations of the amplitude of zero sequence
vector are identical, while the representations of phase displacement differ in each sector and can be summarized as:
• for Sectors I and VI:
!
√
6 (λB − λA )
−1
,
(12)
θ = sin
2∆
•
•
for Sectors II and III:
2π
θ=
+ sin−1
3
√
for Sectors IV and V:
4π
+ sin−1
θ=
3
√
!
6 (λC − λB )
,
2∆
!
6 (λA − λC )
.
2∆
(13)
(14)
Note that, for the case when λA = λB = λC , it is impossible to obtain the amplitude of the injected zero sequence
based on (9) since both the numerator and denominator
become zero. However, it is meaningless to analyze this
situation since no actual power is generated. Furthermore, for
λA = λB = λC > 0, all the numerators and denominators in
(12)–(14) also become zero, but this case represents a balanced
power generation and hence no zero sequence injection is
needed.
III. C ONCEPTS OF C ONVERTER E NERGY BALANCING
L IMIT
In order to redistribute the power among the three phases,
the actual phase voltages should be the combination of the
positive sequence and fundamental frequency zero sequence
(Fig. 2). Therefore, to keep the three-phase balanced currents
injected into the grid with the converter modulated in the linear
region, these phase voltages should not exceed three times
the designed capacitor voltage for a seven-level CHB. Hence,
the energy balancing limit with fundamental frequency zero
sequence injection can be obtained by confining the maximum
phase voltage to three times the capacitor voltage Vc :
√ q
2 Vx2 + Vy2 ≤ 3Vc ,
(15)
Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, TAS, Australia, 29 September – 3 October 2013
where:
• for 0 ≤ θ ≤ π/3 + α or 5π/3 + α ≤ θ ≤ 2π:
•
•
4
TABLE II
PARAMETERS OF THE T HREE - PHASE S EVEN - LEVEL CHB C ONVERTER
Vx = V0 cos θ + Vcp cos α,
(16)
Vy = V0 sin θ + Vcp sin α,
(17)
Peak Power of Single Panel
Values
PV Parameters (W)
64.98
Module Number in a Single String
311
String Number in Parallel
55
for π/3 + α ≤ θ ≤ π + α:
Vx = V0 cos θ + Vcp cos (α + 2π/3) ,
(18)
Vy = V0 sin θ + Vcp sin (α + 2π/3) ,
(19)
for π + α ≤ θ ≤ 5π/3 + α:
Converter Parameters
Values
Grid Voltage, Vg (kV)
6.6
Rated Power, Ppeak (MW)
10
Capacitor Voltage, Vc (V)
2500
IGBT Voltage Rating (V)
3300
1500
Vx = V0 cos θ + Vcp cos (α + 4π/3) ,
(20)
IGBT Current Rating (A)
Vy = V0 sin θ + Vcp sin (α + 4π/3) .
(21)
Filtering Inductor, Lf (mH)
5
Carrier Frequency, f (Hz)
1200
In real applications, all three-phase generation ratios are
variable according to environmental factors and module parameters. Therefore, all points (λA , λB , λC ) satisfying the
above requirements define a space where the zero sequence
injection can rebalance the currents injected to the grid. This
space is defined as the Energy Balanceable Space (EBS).
Operation points lying outside this space are impossible to
maintain three-phase balanced grid currents without forcing
the converter into the over-modulation region.
This EBS space can be numerically obtained by calculating
two surfaces, an upper surface formed by the maximum
balanceable λC max for each given (λA , λB ) and a lower one
formed by the minimum balanceable λC min . Hence, the EBS
of the converter of Table II is plotted in Fig. 3.
Field experience indicates that, in most cases, the maximum
deviation of the power generation ratio in one phase from the
three-phase average value usually falls within 20%. That is
to say scenarios with extremely unbalanced power generation
are quite rare. However, extending the achievable EBS is still
of great significance, since, for the same balanceable space, it
can facilitate operation with lower capacitor voltage and thus
reduction of losses in the DC voltage boosting stage.
IV. E XTENDING THE E NERGY BALANCING L IMIT BY
T HIRD H ARMONIC Z ERO S EQUENCE I NJECTION
Third Harmonic Injection (THI) has been used to improve
the DC voltage utilization of three-phase voltage source
inverter. For balanced operation, the conclusion has been
drawn that the injection level of one sixth of the fundamental
component achieves highest AC output without being into
the over-modulation region. In this section, a third harmonic
injection for unbalanced three-phase system is proposed to
extend the range of achievable AC output voltage and, hence,
the converters EBS.
To provide an indicator of the energy balancing limit of the
converter, the Balance Factor (BF) is defined as the volume
of the EBS:
ZZ
BF =
(λC max − λC min ) dλA dλB .
(22)
0≤λA ,λB ≤1
Fig. 3. Energy Balanceable Space with fundamental frequency zero sequence
injection.
Having noted that each modulation reference derived in
Section II consists of fundamental frequency positive sequence
and fundamental frequency zero sequence, a straightforward
way to find the optimum injection level is by combining
the optimum injection for the positive sequence with that
for the zero sequence together. Consequently, the modulation
reference for Phase A under this Double 1/6 Third Harmonic
Injection (DTHI) method can be rewritten in the following
form:
√
√
2Vcp
Vca =
2Vcp cos (ωt + α) −
cos (3ωt + 3α)
|
{z
} | 6
{z
}
I
√
II
√
2V0
+
2V0 cos (ωt + θ) −
cos (3ωt + 3θ), (23)
|
{z
} | 6
{z
}
III
IV
where Term I stands for the positive sequence and II for its
1/6 third harmonic injection, while Term III and IV represent
the fundamental frequency zero sequence and its 1/6 third
harmonic injection. The EBS is then obtained using a similar
method to the previous section:
max (| vca |max , | vcb |max , | vcc |max ) ≤ 3Vc .
(24)
Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, TAS, Australia, 29 September – 3 October 2013
5
Current(kA)
2
ia
ib
ic
0
−2
0
0.01
0.02
0.03
Time(s)
0.04
0.05
0.06
Voltage(kV)
(a)
10
Vca
Vcb
Vcc
0
−10
0
0.01
0.02
Fig. 4. Energy Balanceable Space with DTHI.
0.03
Time(s)
0.04
0.05
0.06
(b)
Fig. 6. Balanced operation of CHB converter (a) three-phase grid currents
(b) three-phase seven-level converter output voltages.
0.5
0.4
Current(kA)
2
BF
0.3
0.2
Fundamental frequency Zero Sequence Injection
0.1
ia
ib
ic
0
−2
0
0.01
0.02
DTHI
0.03
Time(s)
0.04
0.05
0.06
0
2
4
6
Peak Power (MW)
8
10
Fig. 5. Balance Factor comparison.
The EBS with DTHI for the same converter parameters as
in Table II is plotted in Fig. 4.
V. BALANCE FACTOR C OMPARISON
This section compares the BFs of the two aforementioned
methods numerically. The comparison is shown in Fig. 5 for
the actual peak operating power increasing from 2MW to
10MW, for the 10MW converter designed in Table II. It can be
observed that, for the same method, the BF declines with the
increasing operating power, which means that if required it is
possible to extend the energy balancing limit by oversizing the
converter. Furthermore, the DTHI method increases the BF on
average by 55%, as compared with the fundamental frequency
zero sequence injection.
VI. S IMULATION V ERIFICATION
The two methods of zero sequence injection are investigated
through simulations of the converter with the specifications
given in Table II. Under balanced operation the converter injects symmetrical currents (Fig. 6a) and generates symmetrical
voltages (Fig. 6b).
Then the solar radiation decreases from 1 kW/m2 to 600
kW/m2 on the PV modules of Phase A, corresponding to
58.62% of the rated value for the module adopted in this paper,
while the other two phases are not affected. If no additional
Voltage(kV)
(a)
0
10
Vca
Vcb
Vcc
0
−10
0
0.01
0.02
0.03
Time(s)
0.04
0.05
0.06
(b)
Fig. 7. Unbalanced operation of CHB converter without energy balancing
control (a) three-phase grid currents (b) three-phase seven-level converter
output voltages (λA = 0.5862, λB = λC =1).
balancing control methods are applied, the three-phase grid
currents will be unbalanced, as depicted in Fig. 7a.
Therefore, fundamental frequency zero sequence needs to
be injected according to (9) (10). It can be observed in Fig. 8
that, by distorting the converter output phase voltages, the zero
sequence can successfully redistribute the power among the
three phases as required and maintain the three-phase balanced
grid currents. However, due to the zero sequence injection,
the level of each converter output phase voltage might be
different, which, as a consequence, makes it complicated to
analyze the harmonic spectra. Similarly, the simulation results
employing the presented DTHI are provided in Fig. 9. It can
be observed that by using DTHI the maximum modulation
index becomes lower, which indicates a larger EBS compared
to the fundamental frequency zero sequence injection.
VII. C ONCLUSION
The multilevel cascaded H-bridge converters face the problem of unbalanced power generation as a result of unequal
radiation, temperature and panel parameters, for large-scale
Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, TAS, Australia, 29 September – 3 October 2013
2
ia
ib
ic
0
−2
0
Current(kA)
Current(kA)
2
0.01
0.02
0.03
Time(s)
0.04
0.05
−2
0
0.06
ia
ib
ic
0
0.01
0.02
10
Vca
Vcb
Vcc
0
0.01
0.02
0.03
Time(s)
0.04
0.05
0.06
0.03
Time(s)
0.06
Vca
Vcb
Vcc
0
−10
0
0.01
0.02
0.03
Time(s)
0.04
0.04
0.05
0.06
1
Reference
Reference
0
0.02
0.05
0.05
0.06
(b)
Ref A
Ref B
Ref C
Zero seq.
0.01
0.04
10
(b)
1
−1
0
0.03
Time(s)
(a)
Voltage(kV)
Voltage(kV)
(a)
−10
0
6
Ref A
Ref B
Ref C
Zero seq.
0
−1
0
0.01
0.02
0.03
Time(s)
0.04
0.05
0.06
(c)
(c)
Fig. 8. Unbalanced operation of CHB converter with fundamental frequency zero sequence injection (a) three-phase grid currents (b) threephase seven-level converter output voltages (c) three-phase voltage references
(λA = 0.5862, λB = λC =1).
Fig. 9. Unbalanced operation of CHB converter with DTHI (a) three-phase
grid currents (b) three-phase seven-level converter output voltages (c) threephase voltage references (λA = 0.5862, λB = λC = 1).
photovoltaic farm applications. A third harmonic injection
method for unbalanced three-phase systems, named Double
1/6 Third Harmonic Injection, has been presented in this paper
to extend the converters energy balancing limit. Consequently,
the three-phase balanced currents can be injected into the grid
for more unbalanced power generation. The effectiveness of
the presented method in extending the Energy Balanceable
Space and Balance Factor is verified through computer simulation results.
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