Download Modular multilevel converters with integrated batteries energy storage

3rd The International Conference on Renewable Energy Research and Applications
19-22 Oct 2014 Milwakuee-USA
Modular multilevel converters with integrated
batteries energy storage
A. Lachichi
ABB Corporate Research Centre,
SE-721 78 Västerås, Sweden
[email protected]
Abstract—This paper presents the analysis of the modular
multilevel converter with integrated batteries energy storage and
highlights the influence of the power injected to the grid from the
batteries or vice versa on the capacitors’ voltage balancing. The
control objective of the converter is to maintain a balance
between the arms. By redefining the circulating current in order
to compensate for reactive power and rebalance the ac grid
voltage asymmetries, it is shown through simulation results that
the current injected by the batteries does not introduce any
unbalance to the converter.
Keywords—Batteries energy
converter; STATCOM/BESS
storage;
modular
multilevel
NOMENCLATURE
Cc
Cell capacitance.
iBp/n,I positive/negative-arm current injected to/from the
battery of the ith cell.
ic
circulating current when batteries are not connected to
the cells.
icB
circulating current with batteries connected to the cells.
iv
phase line output current.
ip/n
positive/negative-arm converter current.
Lv
arm inductance.
m
modulation index.
N
Number of cells per arm.
Pac
ac active power.
PB
Batteries power.
Pdc
dc power.
Rv
arm’s resistance.
S
apparent power.
ucm
common mode injection voltage.
ucp/n positive/negative-arm inserted capacitor voltage.
positive/negative-arm total available capacitor voltage.
/
ud
dc bus voltage.
uv
differential voltage.
uvp/n positive/negative-arm voltage.
W
difference of energy between the arms of one leg.
W
total energy of one leg.
W / positive/negative-arm total energy.
positive/negative-arm averaged switching function.
p/n
positive/negative-arm switching function of the ith cell.
p/ni
phase shift of the fundamental line output current with
respect to the fundamental output voltage.
fundamental angular frequency.
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p
i
cm
n
v
phase shift of the fundamental line output current
positive sequence with respect to the fundamental
output voltage positive sequence.
phase shift of the fundamental output common mode
voltage with respect to the fundamental output voltage
positive sequence.
phase shift of the fundamental output voltage negative
sequence with respect to the fundamental output
voltage positive sequence.
I. INTRODUCTION
The integration of batteries energy storage into a
STATCOM is largely used to tackle different gridtransmission problems by providing additional active power
support to the grid. For instance, transient stability and
subsynchronous oscillation damping are improved [1], and
phase jump as well as magnitude fluctuation are reduced [2].
Many studies have been carried out to find the best
approach to connect batteries energy storage into the
STATCOM converter that would optimize not only the size of
the batteries but as well would be a cost effective solution. In
[3], the authors highlight the advantages and disadvantages of
connecting batteries energy storage either in the cascaded
converter or the diode-clamped converter, while in [4], a
sensitive analysis is carried out in order to highlight influence
of the choice of the topology and the network voltage level on
the losses.
Multilevel cascaded converters have made it possible to
integrate batteries energy storage units into the cell of the
topology [5-7]. One of the main benefits of this layout is
undoubtedly the possibility to integrate and adjust the required
active power since each battery unit can operate at different
power level, while maintaining a three-phase balanced line-toline voltage. Moreover, due to its success in HVDC
application, modular multilevel converters are now proposed
as a solution to integrate batteries energy storage into the cell
as exemplified in [8] for solar application. It is demonstrated
in [9] that modular multilevel converters have internal
dynamics which define the behavior of the sum of all
capacitor voltages in one converter arm and the circulating
current which flows between the arms. This inherent
circulating current constitutes a degree of freedom that can be
used in a Statcom/BESS system to compensate the reactive
power and to rebalance the ac grid voltage asymmetries by
3rd The International Conference on Renewable Energy Research and Applications
providing the required active power from the batteries to the
grid. Dynamics of the converter indicate as well the presence
of harmonics components in the arm’s current. Even though it
is possible to reduce the predominant second harmonic
component with the appropriate control strategy, an interface
that would act as a buffer is necessary between the cell of the
converter and the batteries where they are connected to. This
adds to the cost of the overall of the converter. Besides, the
arm’s current oscillates at the fundamental frequency which
could severely damage the batteries if this current is let to flow
into them.
This paper details the analysis of the modular multilevel
converter with batteries energy storage units integrated into
the cells and addresses the problem of imbalance in the phaseleg of a StatCom/BESS system. Firstly, the dynamics of the
converter are presented by taking into account the power
injected from the batteries to the ac grid or vice versa in order
to define the circulating current in steady-state operation of the
converter and show the influence of the batteries’ current upon
the capacitors’ voltage balance and the energy balance
between the phase-arms of the converter. Then the circulating
current is redefined for ac voltage grid asymmetries. The
method used relies on injecting a common mode voltage to
rebalance the ac grid. Finally, a case study is presented to
ascertain the main findings.
II. CIRCUIT DYNAMICS
The modular multilevel converter is conceptually
composed of two traditional cascaded multilevel converters,
stacked one over the other with the middle point forming the
output phase of the converter. As illustrated in Figure 1(a),
where the basic structure of a single phase-leg of an N-level
multilevel converter is shown, the cascaded converter
connected to the positive/negative pole forms the
positive/negative arm. Each arm is formed by an array of a
series-connection of single-phase inverters referred as cells.
Inductors are included within each arm for protection purpose,
etc.
Figure 1(b) depicts a simplified circuit diagram of an
individual cell considered for this analysis. It is composed of
one leg with two IGBTs and their anti-parallel diodes. The
voltage ucp/ni across each capacitor is usually fixed. Both
IGBTs operate in a complementary manner. Moreover, the
cell is said to be either inserted if the upper IGBT is turned on
or the cell is said to be bypassed if the upper IGBT is turned
off. These imply that the cell can insert or bypass its capacitor
to the total array of the capacitors of the converter leg,
synthesizing hence the multilevel waveform. In the particular
case where both IGBTs are turned off, the cell is said to be
blocked and the current flows through the diodes (and through
the capacitor if the latter is to be charged). This particular case
is not considered in this analysis.
Batteries energy storage are connected to the cell via an
interface. For the sake of generality, the batteries and the
interface are modeled as a current source that injects/absorbs a
current to/from the ac grid, regardless of the interface’s
structure as shown in Figure 1(b). The influence of batteries’
characteristics on the performance of the converter is
postponed to future papers.
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A. Circuit dynamics
In this section dynamics equations governing the behavior
of the M2LC with batteries energy storage connected to the
cell are derived.
According to the sign’s convention adopted in Figure 1,
the ac output current is defined as
=
(1)
where ip and in are the positive and negative arm converter
current.
Fig. 1. (a) Phase-leg of the modular multilevel converter. (b) Integrated
batteries energy storage into the cell - equivalent model.
A circulating current containing dc and ac components
flows through the arms due to the voltage ripple of the
capacitors. It maintains the capacitors’ voltage between the
arms balanced. In STATCOM operation of the M2LC, since a
dc voltage between the arms is created, this circulating current
is still present for the same previously stated purpose [10]. In
order to highlight the power exchange from/to the batteries
energy storage, we will differentiate between the circulating
current with and without the energy storage.
The current that flows in the positive/negative arm is hence
defined as
=
=
+
+
+
(2)
,
,
(3)
where ic is the circulating current that flows between the
arms when batteries are not connected to the cells. iBp,i and iBn,i
are the positive and the negative-arm current injected to/from
the battery connected to the ith cell. N-j is the number of cells
with batteries energy storage connected to them. Note that j
could be equal to zero meaning that batteries are connected to
all cells of the arm.
3rd The International Conference on Renewable Energy Research and Applications
By adding (2) and (3), a new circulating current can be
defined. It takes into account the active power exchanged
between the ac grid and the batteries. It is expressed as
=
+(
+
)=
(4)
The dynamics of the arm’s currents are given by
=
=
(5)
,
+
(6)
,
By adding (5) and (6), we obtain the governing equation of
the circulating current icB
,
=
,
,
=
,
(12)
=
B. Control strategy
The main purpose of the open loop control is to find an
expression of
/ which defines the insertion indices np/n in
(9). The method is based on the evaluation of the energy
stored in each arm which makes the control open looped [9].
The time derivative of the stored energy in one arm is
equal to the input power of the corresponding arm which
yields
/
(7)
By subtracting (5) and (6), we obtain the governing
equation of the output current iv
(8)
where = and = are the output phase equivalent
inductance and resistance respectively.
It is worth mentioning that, though the converter is
intended to operate in a STATCOM mode, the dc-grid voltage
is maintained constant thanks to the capacitors’ cell voltage
regulation.
A detailed model which captures all effects that are likely
to be significant for the analysis is generally speaking difficult
to handle and work with. For internal control objectives of the
converter that aim to maintain an energy balance between the
arms, an averaged model is used with the following
assumptions that hold up satisfactory as demonstrated in [11]
An infinite switching frequency is assumed.
An infinite number of cells per arm is assumed.
=
/
=
/
/
(9)
The dynamics equations governing the circulating current
and the ac output current are hence rewritten as
=
=
(10)
(11)
where uv and uc are the voltage that drives the ac output
current and the circulating current respectively. They are
expressed as
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/
/
(13)
/
(14)
On another hand, the energy stored in one arm is expressed
as
=
/
Differentiating (14) and substituting the result in (13)
yields
/
=
/
(15)
cos
(16)
/
The expression of the inserted capacitors’ voltage for each
arm can be deduced from (12). However, to simplify the
analysis they can be defined as
=
=
+
cos
(17)
For the positive arm, substituting (2) and (16) into (15)
yields
=
+
+
(
+
(
cos
) (18)
cos
) (19)
+
(20)
For the negative arm, substituting (3) and (17) into (15)
yields
The voltage balancing between the cells is always
assured.
With these assumptions, by inserting the required number
of cells, the inserted voltage ucp/n in each arm varies from 0 to
/ , and is given by
19-22 Oct 2014 Milwakuee-USA
=
+
The open loop control relies on processing the energy
stored in one leg and the difference of energy between the
positive and negative arm. Hence by adding and then
subtracting (18) and (19), we obtain
=2
=
+
2
cos
+
cos
cos
+
+
cos
(21)
Two cases are considered hereafter depending on whether
the ac grid voltages are balanced or not. The aim of the
analysis is to highlight the influence of the batteries on the
capacitors’ voltage balance and the energy balance between
the phase arms. Henceforth, the expression of the circulating
3rd The International Conference on Renewable Energy Research and Applications
current that will achieve the control objective for both cases is
derived.
Case A
Let us assume that the output phase voltage and current are
quasi-sinusoids, though the output phase current is controlled
using a feedforward controller. They are given by
=
=
cos
)
In the particular case of ac grid unbalance the ac current is
not anymore split equally between the arms. This leads to a
circulating current containing a dc component and an ac
component that oscillates at the fundamental frequency. It can
be defined as
=
(23)
Substituting (23) in (20) and rearranging the terms yields
=2
+
(cos(2
+
+
(25)
cos
(26)
The circulating current is hence given by
=
cos
(27)
Case B
In this case, we shall define the circulating current under
asymmetrical ac grid conditions that will rebalance the
unbalanced ac voltages. Moreover, the development of the
algorithm relies as well on the injection of a common ac
voltage that oscillates at the fundamental frequency as
presented in [12] for the cascaded converter.
The converter phase voltage are hence redefined as
cos(
)+
cos(
+
)+
cos(
+
(28)
Similarly, the converter phase current are redefined as
=
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cos
+
cos(
+
)
(29)
=
)
(
where
=
=
When batteries are providing an active power to the grid,
there is a small reduction in the reactive power supply due to
the quadratic relation between the active and the reactive
power. Hence, the first term in (26) would theoretically be
different from zero. Note that even when batteries are
disconnected, the circulating current should be different from
zero in order to allow a power exchange between the arms.
Hence, for a STATCOM operation of the M2LC, a small
amount of active power should be provided especially when
the converter is absorbing reactive power.
=
,
)
(
and it is given
(31)
)
The common mode voltage is determined by considering
the total phase-leg average power of each phase. It is
expressed as
=
or using the notation icB, it is defined as
=
=
,
(24)
=
(30)
For phase a, we found the expression of
In order to have a stable operation of the converter, i.e., the
capacitor’s voltages remain balanced, the constants in (21) and
(24) should be zeroed. It appears from (21) that iBp should be
equal to iBn which means that the number of batteries energy
rooms connected in the positive arm should be equal to the
number of batteries energy rooms connected in the negative
arm. Hence, we should always satisfy the following
=
cos
by
cos
) + cos )
+
Note that during ac grid asymmetry, the circulating current
is defined for each phase-leg depending on the difference of
power in one phase-leg .
(22)
cos(
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cos
2
)
sin(
)
and tan(
+
cos(
),
=
cos(
cos
sin
+
+
4
3
+
+
2
cos
sin
)=
sin
+
+
4
3
+
sin(
)
III. CASE STUDY
To ascertain the feasibility of the study, a model of the
M2LC with batteries units integrated in each cell has been
implemented in PSCAD with the parameters shown in Table I.
TABLE I. S PECIFICATION OF THE SIMULATED SYSTEM
Apparent power
Batteries energy storage power
Grid voltage
DC-link voltage
Cell capacitance
Nominal cell voltage
Number of cells per arm
60 MVA
35 MW
30 kV
±50kV
2.5 mF
2.5 kV
40
Figure 2 depicts the voltage across each cell when batteries
are injecting active power to the grid at t=0.5s. The
capacitors’ voltage are kept well balanced and are not
influenced by the current injected from the batteries. The
current that is injected by each battery is around 100 A, and it
is reflected in the circulating current as shown in Figure 3. The
value of the discharge current has been chosen in such a way
that the batteries are discharged in roughly 30 min. Figure 4
depicts the active and reactive power for this case.
Similar figures are obtained when batteries are being
charged at t=1.6s. In this particular case, the active power
flows from the ac grid to the batteries. Figure 5 depicts the
voltage across each cell where the voltage is being adjusted.
Figure 6 shows the circulating current which reflects the
3rd The International Conference on Renewable Energy Research and Applications
charging current of a battery room, fixed to 50 A in the
simulation. Figure 7 shows the active and reactive power for
the charging mode.
P [MW]
2
5
0
-2
1.2
4
1.3
1.4
1.5
1.6
t [s]
1.7
1.8
1.9
2
1.3
1.4
1.5
1.6
t [s]
1.7
1.8
1.9
2
-55
Q [Mvar]
ucp,i [kV]
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3
-60
-65
1.2
2
1
0.3
0.4
0.5
0.6
0.7
Figure 7. Charging mode. Active power (top). Reactive power (bottom).
0.8
t [s]
Fig. 2. Discharging mode. Voltage across the cells (positive arm).
200
100
ic [A]
0
-100
-200
-300
0.2
0.3
0.4
0.5
0.6
t [s]
0.7
0.8
0.9
1
IV. CONCLUSION
In this analysis, we have focused on exploring the
capability of the modular multilevel converter with integrated
batteries energy storage through deriving the circulating
current expression to compensate for reactive power and to
rebalance the ac grid voltage asymmetries. Simulation results
showed that batteries can be charged or discharged without
introducing any unbalance to the converter provided that the
same number of batteries’ units is connected to the positive
and negative arm. The capability of the converter to rebalance
the ac grid during asymmetric ac grid conditions is postponed
to future papers.
Fig. 3. Discharging mode. Circulating current for a discharge current of 100A.
REFERENCES
P [MW]
0
[1]
-2
-4
0.2
0.3
0.4
0.5
0.6
t [s]
0.7
0.8
0.9
1
0.3
0.4
0.5
0.6
t [s]
0.7
0.8
0.9
1
Q [Mvar]
-50
-60
-70
0.2
Fig. 4. Discharging mode. Active power (top). Reactive power (bottom).
4
ucp,i [kV]
3.5
3
2.5
2
1.5
1
1.4
1.45
1.5
1.55
1.6
t [s]
1.65
1.7
1.75
Fig. 5. Charging mode. Voltage across the cells (positive arm).
150
ic [A]
100
50
0
-50
1.2
1.4
1.6
1.8
2
2.2
t [s]
Fig. 6. Charging mode.Circulating current for a charge current of 50 A.
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