Este trabalho analisa o desempenho de uma microrede de corrente contínua utilizando a técnica de controle de queda de tensão para regular a tensão da rede e controlar a distribuição de carga entre diferentes fontes. Um modelo da microrede foi implementado no ambiente Simulink/MATLAB, e os resultados das simulações validaram a eficácia da estratégia de controle de queda de tensão com controladores proporcionais e proporcionais-integrais. O estudo conclui que o controlador proporcional apresentou uma resposta mais rápida, enquanto o controlador proporcional-integrais garantiu uma melhor regulação de potência e erro de estado estacionário nulo.

1. Analysis of Voltage Droop Control Method for dc
Microgrids with Simulink: Modelling and
Simulation
Rodrigo A. F. Ferreira1,2
, Henrique A.C. Braga1
, André A. Ferreira1
and Pedro G. Barbosa1
1 Power Electronics and Automation Group 2Electronics and Automation Group
Electrical Engineering Department Federal Institute of Education, Science and
Federal University of Juiz de Fora Technology of Southeast of Minas Gerais
Juiz de Fora, MG Juiz de Fora, MG
36.036-900 Brazil 36.080-001 Brazil
Abstract—This work presents a perfomance study of a
dc microgrid when it is used a voltage droop technique to
regulated the grid voltage and to control the load sharing
between different sources. A small model of a dc microgrid
comprising microsources and loads was implemented in
the Simulink/Matlab environment. Some aspects about
centralized (master–slave) and descentralized (voltage
droop) control strategies as well as the procedures to
design the controllers, with and without droop control,
are presented and discussed. Simulation results obtained
with the digital model of the dc microgrid with three
microsources will be presented to validate the effectiveness
of the voltage droop strategy, applied to proportional and
proportional–integral controllers, to regulate the microgrid
voltage.
Index Terms—dc microgrid, dc-dc converter, voltage
droop control.
I. INTRODUCTION
Microgrid (µG) is a electrical network comprising
loads, microsources (µS) and communication &
automation systems. These µS, also called distributed
sources (DS), increase the offer of energy, the reliability
and the efficiency of electrical power systems since they
are able to operate close to loads and connected to or
not to another electric power network [1].
Nowadays, loads like lighting systems and
electronic equipments (e.g. computers and peripherals
comunication devices, tv sets among others) are
responsable for about 35 % of the electricity
consumption in residential and comercial applications
[2]. All of these loads have a front-end converter to
transform the ac energy to dc. It is expected that this
type of consumption will increase in the near future
with the integration of hybrid electric vehicles (EHV)
into the grid.
In the same way, the most of the alternative energy
sources (e.g. photovoltaics, fuel cells, etc.) as well as
many of the energy storage devices such as batteries,
supercapacitors and superconducting magnetic energy
storage systems (SMES) produce and store electrical
energy in direct current. Thus, the design of dc
microgrids is fundamental since the dc loads and
microsources could be easily integrated on the network.
According to [3], the losses in the dc microgrids will
be lower since there is no skin effect and no reactive
power flow in the dc cables. They have additional
advantages of no need of voltage synchronization and
effect of phase imbalance. However, these systems have
drawbacks related to overcurrent protection, since the
fault currents do not have natural zero crossing [4] and
[5], and with the control the network voltage by reactive
power flow, as it happens in ac systems [6].
Figure 1 shows an example of a generic dc microgrid
with microsources, energy storage systems, dc and ac
loads. Static converters connect all devices to the dc grid.
A dc-ac converter is used as interface between the dc µG
and the ac electric distribution network. This converter
is blocked in the case of islanded operation of the dc
microgrid.
In this scenario, an important issue related to the
operation of dc microgrids is the dc bus voltage
regulation. Two types of voltage control are commonly
used in the literature: master–slave and voltage droop.
The master-slave method depends on the communication
between the interface converters. The master converter
controls the voltage of the dc bus and sends reference

2. Fig. 1. Generic topology of a dc microgrid.
signals to other converters. In the method of voltage
droop, the dc bus voltage is measured at the points of
coupling of the converters and it is used to calculate the
amount of energy that each load or source will consume
or supply.
In [7] it was presented five different methods of
droop control and other control methods that need some
level of communication. In [8] and [9] were proposed
improvements in the voltage droop control using adaptive
control and integral controllers to reduce steady state
errors. In [10], it is proposed a methodology to assure
power sharing between the sources since the power
ratings of the converters are equal.
The main objective of the this work is to present a
comparative analysis of voltage droop control method
using proportional and proportional-integral controllers
to regulate the dc voltage of an isolated dc microgrid.
The dc microgrid, consisting of three dc sources with
their controllers and a variable load was modeled in
the Simulink/Matlab software. Simulation results will
be presented to validate the analysis and the design
proceedures.
II. CONTROL OF PARALLELED CONVERTERS
The paralleling of power sources in microgrid
applications through power electronics modules offers a
number of advantages over the utilization of a single
high power converter [7]. Two different methods can
be used to control paralleled converters on a microgrid:
master-slave and voltage droop [6]. In this section some
particularities of each method will be presented.
A. Master-Slave Control
Figure 2 shows the block diagram of the master-slave
control scheme. In this figure, each block is composed
by a dc source, a static converter and its controller.
The first block, the master module, controls the grid
dc bus voltage while the other blocks, the slaves, are
current controlled. Despite of the fully controllable load
sharing [9], this control scheme has the disadvantage
of needing a fast communication channel since the
reference currents for slave converters are provided by
the master block. The loss of the communication link
or malfuncioning of the master block can shut down the
whole system [7] and [11]. Thus, to avoid or reduce the
probability of failure, this system should be design with
some redundancy.
DC
V
1
I
2
I
n
I
T
I
ref
V
2
ref
I
n
ref
I
DC
V
Fig. 2. Schematic diagrama of master–slave control.
B. Voltage Droop Control
Figure 3 shows the block diagram of the voltage
droop control scheme. Each droop controller emulates
an impedance behavior reducing the converter output
voltage with the increase of the supplied current. This
strategy promotes the current sharing between paralleled
converters connected in the dc microgrid without the
need of a central control [7]. The Fig. 4 shows a detail of
the voltage controller of the dc-dc converter. A low–pass
filter is used to cut-off harmonic frequencies and fast
oscilations of the dc bus voltage.
Based on Fig. 4 it is possible to calculate Pref as
follows [6] and [10]:
Pref = G (s)
Vref −
ωLP
s + ωLP
Vdc
Vdc, (1)

3. DC
V
1
I
2
I
n
I
T
I
ref
V
ref
V
ref
V
Fig. 3. Schematic diagram of voltage droop control.
DC
v
S
v L
i
S
v
DC
v
REF
v REF
i
d
lp
lp
s
ω
ω
+
+
−
REF
V
DC
V
S
V
REF
I
( )
G s
Fig. 4. Voltage control scheme of the dc-dc converter
where G (s) is the transfer function of the compensator,
Vref is the reference voltage, ωLP
is the cutoff frequency
of the low pass filter, and Vdc is the dc grid voltage at
the point of the converter coupling.
From (1) the reference current for each converter can
be calculated as follows,
Iref =
Pref
Vs
, (2)
where Vs is the voltage of the dc source.
III. THE VOLTAGE DROOP DESIGN
The voltage droop scheme can be viewed as a negative
slope in the converter characteristic in the P–V plane. In
this work, two types of controllers, proportional (P) and
proportional–integral (PI), will have their performance
investigated to control paralleled converters connected
to dc microgrid. Despite of the easy implementation of
the P controller it exhibits steady-state errors for step
changes in the reference signal. On the other hand,
converter with a PI controller has the disadvantage
of presenting a poor load sharing due to the integral
characteristic of the compensator [9].
A. Proportional Controller
The proportional controller can be designed to impose
a droop on the operation characteristic of the converter in
similar way as it happens when a dc source has a series a
resistance Rd,n. Thus, the gain kp of the transfer function
can be writtes as,
G (s) = kp =
1
Rd,n
. (3)
where the subscript n indicates the converter number.
Substituting (3) in (1) and assuming 0 dB gain for
the low-pass filter, it is possible to write the expression
bellow for the rated power of the source.
Prated,n = δn (1 − δn)
V 2
ref,n
Rd,n
, (4)
where δn =
1 − Vdc
Vref,n
is the nominal droop or the
relative converter output voltage droop for the rated
power.
Defining Prated,n, Vref,n and δn for each source, it
is possible to calculate the value of Rd,n. A smooth
droop will result in a good voltage regulation to the
converters. However, in this case, they will present a poor
load sharing characteristic. On the other hand, a steep
slope will result in a good load sharing characterisitc
and a poor voltage regulation. From [9] and [10], a good
microgrid performance is achieved for δn in the range
of 2 and 5 %.
Since the controller provides a resistive droop
behavior for the microsource, the dc bus capacitance
may be calculated to force a similar performance of a
Butterworth filter for the dc microgrid [10]. Thus, the
total capacitance at the source converters side of the DC
bus can be calculated by,
Cdc,conv =
4
Rd · ωLP
, (5)

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B. Proportional-Integral Controller
A Proportional–Integral controller given by (6) may
be used to cancel the steady state error.
G (s) = kp
1 +
1
sTi
, (6)
where Ti is the integral time constant of the controller.
The gain of the PI can be determined applying the
methodology used in the P–controller. In [9] the author
calculates the PI time constant by:
Ti =
4
ωLP
. (7)
IV. SIMULINK MODELLING AND SIMULATION
Figure 5 shows the block diagram of the system
modelled in the Simulink/Matlab. It has a resistive load
and three dc sources. Three boost (step–up) converters
connect the sources to the dc microgrid. This converter
does not permit the flow of energy from the grid to the
dc sources. The voltage of the dc microgrid is 750 V.
Figure 6 shows the Simulink block diagram of the
current controller. The output of this block feeds the
hysteresis controller shown in Fig. 7. The hysteresis
controller has a non-linear comparator with a dead
band ∆i to assure a fast and accurate response for the
converter [12]. It was implemented using a m-function
block with a band of ±5 A.
Iref
1
k
-K-
TF
T .s+1
T .s
Pref
P/v
LP Filter
wp
s+wp
vDG
3
vo
2
Vref
1
Fig. 6. Simulink PI block diagram with voltage droop.
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Fig. 7. Simulink hysteresis block diagram.

5. A. Case # 1
In the first case, the dc sources were modelled as
ideal sources and all of them with 200 V and a rated
power equal to 20 kW. The controllers were designed for
Rd,n = 1.34 Ω and Cconvn
= 17 mF and considering
δn = 5 % and ωLP
= 100π rad/s. Table I gives the P
and PI parameters. The reference voltage supplied to the
controller is 750 V .
TABLE I
P AND PI PARAMETERS
Parameter Value
kp (W/V 2
) 0.75
Ti (ms) 12.73
Figure 8 shows the voltage of the dc microgrid and
the behavior of the powers supplied by each converter to
the load for a P and PI controller, respectively. From 0
to 50 ms the microgrid is energized. In t = 250 ms the
value of the power drained by the load is step changed
from 20 kW to 30 kW. Fig. 9 shows the detail of the
microgrid dc voltage and of the converter powers during
the load variation.
Transitory
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
500
1000
DC bus voltage
Vdc
[V]
Time(s)
Vref
P controller
PI controller
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
5
10
Average Power
P
[kW]
Time(s)
Fig. 8. Behavior of the dc bus voltage (top) and average supplied
power (bottom) for balanced dc sources.
Analyzing the results it is possible to conclude that
the P–controller has a faster response. However, the
dc voltage is equal to 740 V before the load step
change and 730 V after. The total power supplied to
the load varies from 19.28 kW to 27.86 kW. On the
other hand, the PI–controller exhibits slower transient
0.25 0.3 0.35 0.4 0.45 0.5
700
750
800
850
DC bus voltage
Vdc
[V]
Time(s)
Vref
P controller
PI controller
0.25 0.3 0.35 0.4 0.45 0.5
6
7
8
9
10
Average Power
P
[kW]
Time(s)
Fig. 9. Detail of the dc bus voltage.
response. However, the steady state error is canceled. For
the PI–controller, the power supplied to the load varies
from 20.05 kW to 29.89 kW in t = 250 ms. Since all
the dc sources are equals the three converters have the
same behavior.
B. Case # 2
In this second study it will be analysed the behavior
of the system for the case of the sources having different
values. The three dc sources voltages are 250 V , 200 V
and 150 V , respectively. All the other parameters are not
changed.
Figure 10 shows the voltage of the dc microgrid and
the behavior of the powers supplied by each converter
to the load for a P and PI controller, respectively.
As in the previous case, the load is step changed in
t = 250 ms. Fig. 11 shows the detail of the dc
voltage and power supplied by each converter. Despite
of the zero steady-state error, the PI–controllers force an
oscillatory behavior for the powers of the sources. This
characteristic indicates that the design of the controller
should be done carefully to avoid unstable operation of
the microgrid.
V. CONCLUSION
This work presented simulation results of a dc
microgrid with droop voltage regulation. Some aspects
of the design of the voltages controllers were presented.
Two types of compensators, with voltage droop, were
investigated. The P–controller exhibited a faster response
while the PI showed a better power regulation and a zero
steady–state error. Both controllers, P and PI, exhibited
a good load sharing characteristic. The voltage droop

6. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
0
200
400
600
800
1000
DC bus voltage
Vdc
[V]
Time(s)
Vref
P controller
PI controller
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-40
-20
0
20
40
Average Power
P
[kW]
Time(s)
Fig. 10. Behavior of the dc bus voltage (top) and average power
(bottom) for imbalanced dc sources.
0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44
700
750
800
DC bus voltage
Vdc
[V]
Time(s)
Vref
P controller
PI controller
0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44
6
8
10
Average Power
P
[kW]
Time(s)
Fig. 11. Detail of the dc bus voltage (top) and supplied power
(bottom) for imbalanced dc sources.
method demonstrated to be a good strategy to share the
currents between different converters without the need
of a central controller. The preliminary results indicates
that this type of control is a good option to integrate
distributed energy sources into a microgrid. Non-linear
control, such as SMC (Sliding Mode Control) has been
investigated to replace the voltage droop scheme.
ACKNOWLEDGMENT
The authors would like to express their gratitude
for the financial support offered by FAPEMIG, CNPq,
CAPES, Federal University of Juiz de Fora and Federal
Institute of Education, Science and Technology of
Southeast of Minas Gerais.
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