2017 19th International Conference on Electrical Drives and Power Electronics
Dubrovnik, 04-06 Oct. 2017
Control of a buck-boost DC-DC power converter
for microgrid energy storage
Mateja Car, Mario Vašak, Vinko Lešić
University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, Croatia
mateja.car@fer.hr, mario.vasak@fer.hr, vinko.lesic@fer.hr
Abstract—In this paper, a bidirectional buck-boost converter
for connecting energy storages to a DC microgrid is presented.
The integration of energy storages into the microgrid allows an
enhanced utilization of renewable energy sources. Therefore, an
efficient control of energy storages and corresponding power
converters is required. Two operating modes of the converter
are considered: current control mode and voltage control mode.
Current control enables efficient charge/discharge process of
energy storages whereas the voltage control is responsible for
maintaining the microgrid bus voltage. Both modes have different
applications in a microgrid operation. An averaged model of the
converter was derived for controller design purposes and utilized
for development of a cascaded contol loop. Controller parameters
are chosen by using the root locus method. The developed model
and control structures are validated through simulations of a
detailed converter model in PLECS.
Index Terms—Power converter, buck-boost, averaged model,
microgrid, current control, voltage control.
I. I NTRODUCTION
Microgrid is a cluster of distributed energy sources, storages
and loads operated in the islanded mode or connected to the
grid. The main advantages are: decreasing transmition losses
by powering local loads, increasing the reliability and stability
since they are able to operate even if disturbances occur in
the main grid. This finally enables enhanced integration of
renewable energy sources such as sun and wind. The biggest
obstacle for renewable energy integration in the main grid
is their intermittent and stohastic nature [1]. Introduction of
energy storages into the microgrid efficiently addresses the
problem by enabling time-shifts between production and consumption, and application of different optimization schemes
like electricity peak shaving or operation and maintenance
cost minimization. This posibilites are being explored in
numerous applications (load and production prediction, control
of cooling/heating systems in buildings, energy management in
railway systems etc.) [2] [3] [4], introducing thus a need for an
efficient control of the storages. To make this possible, viable
control of power converters for charging and discharging
management is required.
The main focus of this paper is the development of an
efficient and fast control of a bidirectional buck-boost DC-DC
converter (See Fig. 1) that connects the electrical storage to a
DC microgrid. This converter is part of the microgrid installed
within Laboratory for Renewable Energy Systems (LARES)
at University of Zagreb Faculty of Electrical Engineering and
978-1-5386-3380-9/17/$31.00
c 2017 IEEE
Computing. The converter is designed to operate in storage
current control mode and DC microgrid voltage control mode.
Other typical converter topologies include bidirectional buck,
boost, buck-boost and inverters, depending on the particular
application [5] [6]. For modelling purposes, averaged model
was chosen because it omits high-frequency ripple in the current and voltage waveforms that appear in switched models [7]
[8]. The conventional control method for DC-DC converters
is usually voltage-mode control [9]. Opposed to the voltagemode control, current-mode control introduces improvements
such as inherent current limiting and easier control system
design [10] [11] [12]. For the modeled converter, current-mode
control is chosen and voltage control is achieved indirectly
through a cascaded control loop. The model of the converter
and the designed controllers were compared with a detailed
converter model made in PLECS, a simulation platform for
power electronics.
By directly controlling the storage current and consequently
the State of Charge (SoC) of the batteries, further utilization
towards optimization goals is enabled. On the other hand, in
voltage control operation, different scenarios of microgrid operation in terms of distributed and centralized voltage control
configuration are possible [3] [13] [14] [15]. Considered topology, together with designed controllers, therefore introduces
great flexibility of system configuration and operation, and
opens possibility to higher levels of control.
This paper is structured as follows. In Section II, an averaged model of the converter is derived. The model is further
utilized as a basis for controller design in Section III. Both
inner and outer loop controllers for both operation modes
are designed. Validation of the developed control algorithm
is given in Section IV. Finally, Section V concludes the paper.
II. AVERAGED MATHEMATICAL MODEL
The considered converter is a bidirectional buck-boost type
that consists of two mirrored bidirectional buck topology converters and a common higher voltage DC bus. The considered
DC/DC converter is shown in Fig. 1.
Since both sides are bidirectional, they can operate in buck
or boost mode, depending on the current flow. This way, both
V1 and V2 are flexibile and able to ensure the voltage of up to
the value Vbc . In this paper, we consider V1 as a storage-side
voltage for controlling of charge/discharge process of batteries,
fuel-cells and supercapacitors. Voltage V2 is the microgrid
voltage of 48 V rated value. If the refrence current directions
2017 19th International Conference on Electrical Drives and Power Electronics
Dubrovnik, 04-06 Oct. 2017
MICROGRID SIDE
STORAGE SIDE
is1
is2
+
L1
istorage
+
-
v1
C1
iL1
vL1
S2
S1
d1
RL1
++
Vbc
vx1 S3
-
-
Cbc
d2
RL2
iL2
++
S4 vx2
-
-
L2
vL2
OUTPUT
LOOP
iug
-
+
C2
v2
-
Fig. 1. DC/DC converter scheme
of both sides are defined as in Fig. 1, both the microgridside and the storage side are modeled as buck converters.
In an ideal buck converter, the inductor voltage and current
are represented as in Fig. 2, where the voltage vLj represents
the voltage drop on the inductor Lj and its corresponding
resistance RLj . The objective is to control the average value
of the inductor current and the corresponding transfer function
is required. Since the averaged values of inductor voltage and
current depend on the duty cycle, it needs to be incorporated
in the model. The differential equation of the output loop of
a buck converter is given by:
v̄xj = Lj
dīLj
+ RLj īLj + v̄j ,
dt
v̄xj = dj v̄bc .
(1)
(2)
The voltage v̄xj from (1) is then substituted by (2)
dīLj
+ RLj īLj + v̄j ,
dt
vbc-vj
0
dj T
T
-vj
iLj
j = 1, 2,
where bar notation represents average values and the index
j indicates that the same expression is used for both the
microgrid and the storage side of the converter (see Fig. 1).
Since the converter is connected to a microgrid, no load is
modelled in the output loop but it is replaced with a constant
voltage value (microgrid voltage). The same approach was
used on the storage side. The average switch voltage, v̄xj is
shown in Fig. 3 and its value is calculated by integrating over
one period:
v̄bc dj = Lj
vLj
j = 1, 2.
(3)
Both DC link voltage and the duty cycle are variable, which
is denoted by lower-case letters. The equation (3) is linearized
around the operating point value Vbc0 and a transfer function
between the duty cycle and the inductor current is:
iLmax
iL
iLmin
0
djT
T
Fig. 2. Inductor voltage and current
Gp,j =
I¯Lj (s)
Vbc0
=
,
Dj (s)
sLj + RLj
j = 1, 2.
(4)
where I¯Lj and Dj are Laplace transforms of small changes of
the mean inductor current and the duty cycle, with respect to
their values in the operating point.
The transfer function from (4) is suitable for further design
of the current controller as will be elaborated later. The
DC bus voltage control is then enforced through a cascade
control form as an outer control loop (see Fig. 4). In Fig. 4,
PWM1 denotes the driving block for generating pulse width
2017 19th International Conference on Electrical Drives and Power Electronics
vxj
Dubrovnik, 04-06 Oct. 2017
dv̄bc
= −d1 īL1 − d2 īL2 .
(7)
dt
Negative sign in (7) is added to īL1 because its reference
direction is opposite to the reference direction of the switch
current as in Fig. 1.
Since only the grid side inductor current īL2 is included in
the DC link control, a relation between this current and the
DC voltage is derived, after linearization around a steady state
duty cycle:
Cbc
vbc
vx
dj T
T
D20
V̄bc (s)
=−
.
Gp,dc = ¯
sCbc
IL2 (s)
isj
iLmax
iLmin
is
djT
T
iL2
iL2 reg
iL2 ref
vbc ref
where D20 is the value of d2 in the operating point.
In the same way, the microgrid voltage is controlled in a
cascade structure by setting a reference value for the inductor
current on the storage side, īL1 . Therefore, it is necessary to
link these two variables. Current through the capacitor on the
microgrid side is expressed as:
dv̄2
= īL2 − īug ,
(9)
dt
where īug is the current flowing into the microgrid. The inductor current from (9) is put into (7) and, with the assumption
of constant v̄bc , the following transfer function is obtained to
relate the microgrid voltage with the storage inductor current:
C2
Fig. 3. Switches S3 or S4 voltage and switches S1 or S2 current over one
period
vbc
(8)
PWM2
V̄2 (s)
D10 1
Gp,v2 = ¯
=−
.
D20 sC2
IL1 (s)
vbc reg
(10)
III. C ONTROLLER DESIGN
iL1
v2
v2 ref
iL1 ref
v2 reg
iL1 reg
PWM1
c
iL1 ref
Fig. 4. Converter control scheme. Variable c denotes the control signal that
switches between the current control mode and microgrid voltage control
mode.
modulation (PWM) switching signals for switches S1 and S3 ,
while PWM2 generates signals for switches S2 and S4 . Signals
with index ’ref’ denote reference values for controllers of
the respective variables. Following from this, a relation that
connects the inductor current with DC bus voltage is required.
The DC bus voltage dynamics is given below:
dv̄bc
= īs1 − īs2 .
(5)
dt
The average switch current is shown in Fig. 3 and equals
to:
As mentioned in previous sections, the converter operates
in buck and boost modes. A simplified control scheme is
shown in Fig. 4. The microgrid-side converter is responsible
for maintaining the DC link voltage by setting a reference
value for the microgrid-side current. In current control mode,
the storage current reference value is set from the higher level
microgrid controllers, whereas in voltage control mode it is set
thorugh a cascade control structure responsible for mantaining
the microgrid voltage level.
A. Current control loop
In Section II, the transfer function between the inductor
current and the duty cycle was derived. The duty cycle is
generated by PWM.
The open loop transfer function can then be written as:
G0,i = GRi GP W M Gdelay Gp ,
(11)
Cbc
īsj = dj īLj ,
j = 1, 2.
(6)
By substituting the currents in (5), a nonlinear model is
obtained:
GP W M =
Dj (s)
1
=
,
vcontrol,j (s)
VP
Gdelay =
1
,
s T2 + 1
(12)
where VP is the peak voltage value for comparison with the
triangular reference waverform in the PWM generator and T is
the switching period of the PWM carrier signal, and Gp is the
process transfer function from (4). The controller time constant
2017 19th International Conference on Electrical Drives and Power Electronics
IL,ref
+
-
GR
vcontrol
GPWM
D*
Gdelay
D
GP
IL
Dubrovnik, 04-06 Oct. 2017
Controller parameters were obtained using the same approach as for the DC voltage control loop.
IV. S IMULATION RESULTS
Fig. 5. Current control loop block diagram
was chosen to compensate the dominant process time constant
(TI,i = Lj /RLj ) and the controller gain KR,i is chosen to
follow the magnitude optimum approach, and further tuned
by using a root locus approach to obtain fast dynamics and
desired level of robustness as will be described later. This
controller is used for controling the currents on both sides.
The control loop block diagram is shown in Fig. 5.
B. DC voltage control loop
Since the DC voltage is controlled in a cascade, microgrid
current control loop dynamics are added to the voltage control
loop. The DC voltage open loop dynamics are therefore:
V̄bc (s) I¯L2 (s)
= GR,dc Gp,dc Gci .
G0,dc = GR,dc ¯
IL2 (s) I¯L2,ref (s)
5
×10 RootLocusEditorforOpenLoop1(OL1)
200
(13)
Open-LoopBodeEditorforOpenLoop1(OL1)
The developed averaged model of the converter was compared with the model created in PLECS. Figure 7 shows
step responses for the inductor current, DC bus voltage and
microgrid voltage. Converter parameters are given in Table I.
Averaged model responses are denoted with the red line
and simulation results with a black line. The control loop
was modeled in continuous time domain. The steps that
can be seen in all three responses are a consequence of
PLECS solver that samples at a rate of 50 µs. The current
control loop shows almost identical results both in theory
and in PLECS simulation. Voltage control loops show slight
differences caused by the presence of parasitic resistances
placed in series with the capacitors required in the PLECS
model for physicality purpose, which are not included in the
derived model due to simplicity and negligibile influence. This
resistance is given in Table I as Resr . Beside the parasitic
resistances, the differences are also caused by the battery- and
grid- side converters coupled behavior in affecting the vbc and
the linearization influence of the chosen duty cycle. Because of
all this neglected dynamics, the voltage controller gains were
reduced 10 % in order to increase robustness. The controller
parameters are given in Table II.
100
TABLE I
S IMULATION PARAMETERS
0
0
-5
-10
100
-5
0
BodeEditorforClosedLoop1(CL1)
5
×104
Parameters
L1 , L2
RL1 , RL2
C1 , C2
Cbc
Resr
Tsw
Vp
-100 G.M.: 22.8 dB
Freq: 4.31e+03 rad/s
Stable loop
-200
-90
0
-135
-100
-200
0
-180
-225
-180
-360
100
Values
70 µH
4 mΩ
4000 µF
6000 µF
4 µΩ
50 µs
1V
102
104
P.M.: 40.8 deg
Freq: 1.01e+03 rad/s
-270
106
105
100
Frequency (rad/s)
105
1010
Frequency (rad/s)
Fig. 6. DC bus voltage controller design
The initial PI controller parameters for the system from (13)
are obtained using an automated PID tuning to achieve balance
between performance and robustness by adjusting bandwith
and phase margin. The controller gain is then tuned graphically
by using root locus method (see Fig. 6) [16] in order to achieve
at least two times slower dynamics than the current loop which
is necessary for cascaded control.
C. Microgrid voltage control loop
Microgrid voltage is also controlled indirectly through the
inductor current, i.e. the storage-side inductor current. The
open loop transfer function is given by:
V̄2 (s) I¯L1 (s)
= GR,v2 Gp,v2 Gci .
G0,v2 = GR,v2 ¯
IL1 (s) I¯L1,ref (s)
(14)
TABLE II
PI CONTROLLER PARAMETERS
Controller
Current controller
Microgrid controller
DC link controller
Gain
0.001
-0.9888
-35
Integral time constant
0.0175 s
0.014 s
0.07 s
Figures 9 and 10 are obtained by simulating converter
performance over several operating points in PLECS. The
variable ’control signal’ switches between converter current
mode operation (value ’0’) and microgrid voltage control
(value ’1’) as in Fig. 4. Microgrid voltage is modeled as a
controllable voltage source and represents the voltage maintained by one of the other elements in the microgrid while the
modeled converter operates in current mode. In voltage control
mode, the voltage source is disconnected (see Fig. 8) and the
controllable current source i∗ represents the conditions in the
rest of the microgrid (sum of all currents). The current source
represents converters operating in current control mode in both
2017 19th International Conference on Electrical Drives and Power Electronics
c
1.5
MAT LAB
PLECS
1
2
2.002
2.004
2.006
2.008
i L 1,ref [A]
i L 2 [A]
2
2.01
vbc [V]
t [s]
Dubrovnik, 04-06 Oct. 2017
1
0.5
0
0
0.5
1
1.5
2
t (s)
2.5
3.5
4
0
0.5
1
1.5
2
2.5
3
3.5
4
2.5
3
3.5
4
2.5
3
3.5
4
2.5
3
3.5
4
2.5
3
3.5
4
2.5
3
3.5
4
2.5
3
3.5
4
10
5
0
-5
g
t (s)
i [A]
67
MAT LAB
PLECS
66
5
5.005
5.01
5.015
10
5
0
0
5.02
0.5
1
1.5
i L 1 [A]
49.5
49
10
0
-10
0
MAT LAB
PLECS
48
3.005
3.01
3.015
3.02
3.025
0.5
1
1.5
2
t (s)
i L 2 [A]
48.5
3
2
t (s)
t [s]
vug [V]
3
3.03
t [s]
10
0
-10
0
0.5
1
1.5
2
t (s)
iug
0.5
1
1.5
2
vbc [V]
t (s)
+
C2
10
0
-10
0
v2
-
67
66
65
0
+
-
0.5
1
1.5
2
t (s)
v*
i*
v2 [V]
iL2
i ug [A]
Fig. 7. Step responses
50
45
0
c
Fig. 8. Simulation environment equivalent circuit for voltage and current
control mode.
simulation scenarios. At the beginning of the simulation, the
converter is operating in the current control mode. This is
observable by comparing the manually set inductor current
reference value iL1,ref with the measured current iL1 . After
2.3 s, the control mode switches to voltage control mode.
This switch is followed by a change in currents directions
and values. In this mode, the inductor currents adapt to the
conditions in the microgrid represented by a current source
i∗ . In microgrid voltage control mode, the main goal is to
maintain the microgrid voltage, which may be observed in
figures 9 and 10.
There is a noticable voltage drop when the control signal c
changes. The control loop reacts and changes the inductor
current value in order to increase the microgrid voltage. After
the transient, the microgrid side inductor current, iL2 , is equal
to the microgrid current, iug . Positive signs of currents iug and
iL2 represent energy flow from the storage to the microgrid
and vice versa. The positive sign of the current iL1 , on the
other hand, represents current flow from the microgrid to
the storage. This is consequential to the reference direction
chosen for modeling (see Fig. 1). Changes in the microgrid,
0.5
1
1.5
2
t (s)
Fig. 9. Simulation results, part 1
represented by the current source i∗ , are followed by changes
in converter current values. After switching back to the current
control, the converter tracks the set reference. Disturbance
in microgrid voltage was also simulated at 7.3 s. Microgrid
voltage value was decreased by 0.2 V. This causes a hardly
noticable transient in both inductor currents. After the transient
both currents return to the reference values.
V. C ONCLUSION
The paper elaborates control of a bidirectional buck-boost
converter for integrating electrical storage into a DC microgrid.
Step by step mathematical model is derived and further used
for controllers design of cascaded inductor current loop and
outer DC bus voltage control loop. Two modes of operation are
covered: current control that enables efficient charge/discharge
of an electric storage and voltage control mode for maintaining
the microgrid DC bus voltage. Performed simulations show the
flexibility and fast response of the considered DC converter
topology supported by the developed control scheme.
2017 19th International Conference on Electrical Drives and Power Electronics
Dubrovnik, 04-06 Oct. 2017
c
R EFERENCES
1
0.5
0
4
4.5
5
5.5
6
6.5
7
7.5
8
6.5
7
7.5
8
6.5
d n
o mod
7
7.5
8
6.5
7
7.5
8
6.5
7
7.5
8
6.5
7
7.5
8
6.5
7
7.5
8
6.5
7
7.5
8
i L 1,ref [A]
t (s)
10
5
4
4.5
5
5.5
6
t (s)
i [A]
5
0
-5
-10
4
4.5
5
5.5
6
iL 1 [A]
t (s)
10
5
0
-5
4
4.5
5
5.5
6
i L 2 [A]
t (s)
0
-10
4
4.5
5
5.5
6
i ug [A]
t (s)
5
0
-5
-10
4
4.5
5
5.5
6
vbc [V]
t (s)
66.5
66
65.5
4
4.5
5
5.5
6
v2 [V]
t (s)
50
48
4
4.5
5
5.5
6
t (s)
Fig. 10. Simulation results, part 2
ACKNOWLEDGMENT
This work has been supported by the Croatian Science
Foundation under the project No. 6731 - Control-based Hierarchical Consolidation of Large Consumers for Integration
in Smart Grids (3CON, http://www.fer.unizg.hr/3con).
[1] F. Farzan, S. Lahiri, M. Kleinberg, K. Gharieh, F. Farzan, and M. Jafari,
“Microgrids for fun and profit: The economics of installation investments
and operations,” IEEE Power and Energy Magazine, vol. 11, no. 4, pp.
52–58, 2013.
[2] V. Lešić, A. Martinčević, and M. Vašak, “Modular energy cost optimization for buildings with integrated microgrid,” Applied Energy, vol. 197,
pp. 14 – 28, 2017.
[3] M. Gulin, M. Vašak, and M. Baotić, “Analysis of microgrid power flow
optimization with consideration of residual storages state,” pp. 3126–
3131, 2015.
[4] H. Novak, M. Vašak, and V. Lešić, “Hierarchical energy management of
multi-train railway transport system with energy storages,” pp. 130–138,
2016.
[5] T. Dragičević, X. Lu, J. C. Vasquez, and J. M. Guerrero, “DC microgrids
- part II: A review of power architectures, applications, and standardization issues,” IEEE Transactions on Power Electronics, vol. 31, no. 5,
pp. 3528–3549, 2016.
[6] K. Tytelmaier, O. Husev, O. Veligorskyi, and R. Yershov, “A review of
non-isolated bidirectional dc-dc converters for energy storage systems,”
pp. 22–28, 2016.
[7] T. Pavlović, T. Bjažić, and Ž. Ban, “Simplified averaged models of
DC-DC power converters suitable for controller design and microgrid
simulation,” IEEE Transactions on Power Electronics, vol. 28, no. 7,
pp. 3266–3275, 2013.
[8] D. Maksimovic, A. M. Stankovic, V. J. Thottuvelil, and G. C. Verghese,
“Modeling and simulation of power electronic converters,” Proceedings
of the IEEE, vol. 89, no. 6, pp. 898–912, 2001.
[9] R. Erickson and D. Maksimović, Fundamentals of Power Electronics,
2nd ed. Kluwer Academic Publishers, 2003.
[10] L. Dixon, Average Current-Mode Control of Switching Power Supplies
Unitrode Application Note. Texas Instruments, Inc., 1997.
[11] P. R. K. Chetty, “Cieca: Application to current programmed switching
DC-DC converters,” IEEE Transactions on Aerospace and Electronic
Systems, vol. AES-18, no. 5, pp. 538–544, 1982.
[12] J. Li and F. C. Lee, “New modeling approach and equivalent circuit
representation for current-mode control,” IEEE Transactions on Power
Electronics, vol. 25, no. 5, pp. 1218–1230, 2010.
[13] Y. Riffonneau, S. Bacha, F. Barruel, and S. Ploix, “Optimal power
flow management for grid connected pv systems with batteries,” IEEE
Transactions on Sustainable Energy, vol. 2, no. 3, pp. 309–320, 2011.
[14] P. Malysz, S. Sirouspour, and A. Emadi, “An optimal energy storage
control strategy for grid-connected microgrids,” IEEE Transactions on
Smart Grid, vol. 5, no. 4, pp. 1785–1796, 2014.
[15] M. Gulin, M. Vašak, and T. Pavlović, “Dynamical behaviour analysis of
a DC microgrid in distributed and centralized voltage control configurations,” pp. 2365–2370, 2014.
[16] W. R. Evans, “Control system synthesis by root locus method,” Transactions of the American Institute of Electrical Engineers, vol. 69, no. 1,
pp. 66–69, 1950.