Analysis of Voltage Droop Control Method for dc Microgrids with Simulink: Modelling and

Simulation

Rodrigo A F. Ferreira1,2, Henrique AC. Braga1, Andre A Ferreira1 and Pedro G. Barbosa1

1 Power Electronics and Automation Group

Electrical Engineering Department

Federal University of Juiz de Fora

Juiz de Fora, MG

36.036-900 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 SimulinklMatlab 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. INTRODUCT ION

Microgrid (fJG) is a electrical network comprising

loads, microsources (fJS) and communication & automation systems. These fJS, 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

2Electronics and Automation Group

Federal Institute of Education, Science and

Technology of Southeast of Minas Gerais

Juiz de Fora, MG

36.080-001 Brazil

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

micro grids 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 micro grid

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 fJG

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

DeBUS Grid

-

-

Fig. 1. Generic topology of a dc micro grid.

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 SimulinklMatlab software. Simulation results will

be presented to validate the analysis and the design

proceedures.

II. CONTROL OF P AR ALLELED CON VERTERS

The paralleling of power sources in micro grid

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.

:"M-asie------------' I r :-4 1 Module : v"

1 f---' i VDci #1 1 1 l ___ _

1----ISlave : #1 1 1 1 1 l ___ _

1----ISlave : #n-1 1 1 1 1

1 -.==J.--l---

1

-,[ , 12 1 ----.

Module 1 #2 1 1 ref2 1 1 1

----------------------, T

:� Module 1

� 1

#n 1 reIn 1 l ________________ I

DC BUS

IT ----.

jVDC LOAD

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 micro grid 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 Pre! as

follows [6] and [10]:

Pre! = G (8) [Vre! - ( WLP ) VdC] Vdc, (1) 8 +WLP

I � Module

..... #1

12 ----.

Module ...... #2

In ----"-+

DeBUS

IT ----.

TVDC LOAD

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

..... Module #n vr�r similar way as it happens when a dc source has a series a

Fig. 3. Schematic diagram of voltage droop controL

DC SOURCE

Low-pass filter

- -

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, W LP 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,

Pref Iref = Vs ) where Vs is the voltage of the dc source.

III. THE VOLTAGE DROO P DESIGN

(2)

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

resistance Rd,n. Thus, the gain kp of the transfer function

can be writtes as,

1 G (s) = kp = R. d,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.

" ( " ) v;.�f,n Prated,n = Un 1 - Un y- ) d,n

(4)

where <5n = (1 - T }!,IC ) is the nominal droop or the

Vref ,n

relative converter output voltage droop for the rated

power.

Defining Prated,n, Vref,n and <5n 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

micro grid performance is achieved for <5n 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,

4 Cdc,conv = R d· wLP

(5)

� � -"

MeaoValue 2

Fig. 5. Simulink dc microgrid model.

B. Proportional-Integral Controller A Proportional-Integral controller given by (6) may

be used to cancel the steady state error.

G (s) = kp [1 + S�i ] , (6)

where � 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:

4 Ti = --.

wLP IV. S IMUL INK MODELL ING AND S IMUL AT ION

(7)

Figure 5 shows the block diagram of the system

modelled in the SimulinklMatiab. 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 D.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.

�.K-

� Vref

lOG

P/v Iref

Fig. 6. Simulink P I block diagram with voltage droop.

Fig. 7. Simulink hysteresis block diagram.

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 nand Cconvn = 17 mF and considering

on = 5 % and wLP = lOOK radj 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/V2) Ti (ms )

Figure 8 shows the voltage of the dc micro grid 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

micro grid dc voltage and of the converter powers during

the load variation.

DC bus I.Qltage

� 500 <.) -0 > --Vref

-- P controller

----- PI controller

0 0 0.05 0.1 0.1 5 0.2 0.25 0.3 0.35 0.4 0.45 0.5

1ime(s)

Al.erage Power

1ime(s)

Fig. 8. Behavior of the de bus voltage (top) and average supplied power (bottom) for balanced de 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

DC bus I.Qltage 850

--Vref

-- P controller _ 800 ----- PI controller G

<.) -0 > 750

700 0.25 0.3 0.35 0.4 0.45 0.5

1ime(s)

Al.erage Power 1 0

9

$ 8 6 Cl.

7

6 0.25 0.3 0.35 0.4 0.45 0.5

1ime(s)

Fig. 9. Detail of the de 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

micro grid 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

DC bus ""Itage 1000 800

� 600 "

." 400 >

200 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

lime(s)

AI<!rage Power

lime(s)

Fig. 10. Behavior of the dc bus voltage (top) and average power (bottom) for imbalanced dc sources.

800 � .g 750 >

700

DC bus I<)ltage

r+ --Vre! -- 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 lime(s)

AI<!rage Power

10 l-; ------: -"��""""'"""'!" "'''';-''''''''"J,er.j:);C�'",",,'''N'''-'''<P",'�. - ' "I'

� 8 L ff���·�'�-��:'���� l",.,W · 6�) u i u i u j u l uui u i u i u l u )u 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

lime(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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