Aalborg Universitet
DC Microgrids – Part I
A Review of Control Strategies and Stabilization Techniques
Dragicevic, Tomislav; Lu, Xiaonan; Quintero, Juan Carlos Vasquez; Guerrero, Josep M.
Published in:
I E E E Transactions on Power Electronics
DOI (link to publication from Publisher):
10.1109/TPEL.2015.2478859
Publication date:
2016
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Dragicevic, T., Lu, X., Quintero, J. C. V., & Guerrero, J. M. (2016). DC Microgrids – Part I: A Review of Control
Strategies and Stabilization Techniques. I E E E Transactions on Power Electronics, 31(7), 4876 - 4891.
https://doi.org/10.1109/TPEL.2015.2478859
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Abstract - This paper presents a review of control strategies,
stability analysis and stabilization techniques for DC microgrids
(MGs). Overall control is systematically classified into local and
coordinated control levels according to respective functionalities
in each level. As opposed to local control which relies only on
local measurements, some line of communication between units
needs to be made available in order to achieve coordinated
control. Depending on the communication method, three basic
coordinated control strategies can be distinguished, i.e.
decentralized, centralized and distributed control. Decentralized
control can be regarded as an extension of local control since it is
also based exclusively on local measurements. In contrast,
centralized and distributed control strategies rely on digital
communication technologies. A number of approaches to using
these three coordinated control strategies to achieve various
control objectives are reviewed in the paper. Moreover,
properties of DC MG dynamics and stability are discussed. The
paper illustrates that tightly regulated point-of-load (POL)
converters tend to reduce the stability margins of the system since
they introduce negative impedances, which can potentially
oscillate with lightly damped power supply input filters. It is also
demonstrated how the stability of the whole system is defined by
the relationship of the source and load impedances, referred to as
the minor loop gain. Several prominent specifications for the
minor loop gain are reviewed. Finally, a number of active
stabilization techniques are presented.
Index Terms - DC microgrid (MG), local control, coordinated
control, impedance specifications, stability.
NOMENCLATURE
Acronyms
AVP Adaptive voltage positioning.
BLDC Brushless DC.
CC Central controller.
CPL Constant power load.
DBS DC bus signaling.
DCL Digital communication link.
DG Distributed generator.
DPS Distributed power system.
EET Extra element theorem.
ESAC Energy storage analysis consortium.
ESS Energy storage system.
EV Electric vehicle.
GM Gain margin.
Department of Energy Technology, Aalborg University, Denmark (email:
tdr@et.aau.dk, juq@et.aau.dk, joz@et.aau.dk).
Xiaonan Lu is with Energy Systems Division, Argonne National
Laboratory, Lemont, IL, USA (email: xlu@anl.gov).
GMPM Gain margin and phase margin.
LC Local controller.
MG Microgrid.
MPPT Maximum power point tracking.
OA Opposing argument.
PCC Point of common coupling.
PD Proportional-derivative.
PI Proportional-integral.
PLC Power line communication.
PLS Power line signaling.
PM Phase margin.
POL Point of load.
PR Proportional-resonant.
PV Photovoltaics.
RES Renewable energy source.
RHP Right-half plane.
TF Transfer function.
VR Virtual resistance.
Variables and Operators
b
i
(t) Input bias of node #i.
C POL converter filter capacitor.
D POL converter steady state duty cycle.
G
c
(s) Transfer function of the voltage controller.
G
vd
(s) Transfer function describing the relation
between converter duty ratio and output
voltage.
G
vg
(s) Transfer function describing the relation
between line disturbance and output voltage.
G
vd,filt
(s) Transfer function describing the relation
between converter duty ratio and output voltage
after the application of input filter.
H(s) Voltage sensor gain.
i
POL
Input current of the POL converter.
i
load
Output current of the POL converter.
L POL converter inductance.
m
p
, m
c
Droop coefficients with power or current
feedback.
N
i
Set of nodes adjacent to node #i.
P
oi
Output power of converter #i.
i
oi
Output current of converter #i.
P DC load power.
P
loadi
Output power of POL converter #i.
P
source
Source power.
R Load resistance.
R
inc
POL converter incremental resistance.
DC MicrogridsPart I: A Review of Control
Strategies and Stabilization Techniques
Member, IEEE, Xiaonan Lu, Member, IEEE, Juan C. Vasquez, Senior Member,
IEEE and Josep M. Guerrero, Fellow, IEEE
R
L
Series resistance of the filter inductor.
SoC State of charge.
s Laplace operator.
T(s) Loop gain of the POL converter control loop.
T
MLG
(s) Minor loop gain.
v
DCi
*
DC link voltage reference value of converter #i.
v
DC
*
Nominal DC link voltage.
v
DC
DC link voltage.
v
ref
Reference value of the load voltage.
v
s
DC source voltage.
v
load
Load voltage.
1/V
m
PWM gain.
x
i
(t) Variable of interest in node #i used in
consensus algorithm.
Z
N
(s) Input impedance of the POL converter if
control loop operates ideally (closed loop input
impedance in low frequency region).
Z
D
(s) Input impedance of the POL converter without
control loop (open loop input impedance).
Z
in
(s) Closed loop input impedance of the POL
converter in the whole frequency region.
Z
out
(s) Open loop output impedance of the POL
converter.
Z
s
(s) Output impedance of the source.
Θ Graph Laplacian of the communication
network.
θ
ij
Elements of Θ.
I. INTRODUCTION
nvironmental concerns and reduction of fossil fuel
reserves gave rise to a growing increase in the
penetration of distributed generators (DGs) that include
renewable energy sources (RESes), energy storage systems
(ESSes) and new types of loads like electric vehicles (EVs)
and heat pumps in the modern power systems. However, these
new components may pose many technical and operational
challenges should they continue to be integrated in an
uncoordinated way, as is the case today. Appearing in large
numbers and scattered across the large geographical areas of
interconnected networks, some of the most prominent
conditions include deteriorated voltage profile, congestions in
transmission lines and reduction of frequency reserves [1].
The idea of merging small variable nature sources with
ESSes and controllable loads into flexible entities that are
called microgrids (MGs) has been presented more than a
decade ago [2], as a possible solution to achieve more
traceable control from the system point of view. MGs can
operate autonomously or be grid-connected and, depending on
the type of voltage in the point of common coupling (PCC),
AC and DC MGs can be distinguished [3]. While remarkable
progress has been made in improving the performance of AC
MGs during the past decade [4][11], DC MGs have been
recognized as more attractive for numerous uses due to higher
efficiency, more natural interface to many types of RES and
ESS, better compliance with consumer electronics, etc. [12].
Besides, when components are coupled around a DC bus, there
are no issues with reactive power flow, power quality and
frequency regulation, resulting in a notably less complex
control system [13][18].
DGs are connected to a DC MG almost exclusively through
a controllable power electronic interface converters and
regulation of the common DC bus voltage is the main control
priority. Droop control is a popular method of achieving this
by means of cooperative operation among paralleled
converters without digital communication links [17], [19]. The
method is based on adding a so-called virtual resistance (VR)
control loop on top
allows current sharing, while providing active damping to the
system and plug and play capability at the same time [20], [21].
However, in spite of these attractive features, there are
several drawbacks that limit the applicability of droop in its
basic shape. The most important ones are load-dependent
voltage deviation and the fact that propagation of voltage error
along resistive transmission lines causes deterioration of
current sharing. A secondary controller needs to be
implemented in order to restore the voltage and tertiary
controller so as to ensure precise current flow among different
buses [12]. There are several options on how to implement this
controller. As for that, while the conventional approach uses a
centralized controller which collects information from all units
via low-bandwidth digital communication links (DCLs) [3], a
very active field of research is focused on resolution of these
problems via distributed control
1
[22], [23]. As a way to
realize various distributed control strategies, the application of
consensus algorithms in DC MGs has recently emerged as a
popular and fashionable approach [22], [24], [25].
Another problem with the basic droop method is its
inability to achieve coordinated performance of multiple
components with different characteristics (i.e., ESSes, RESes,
utility mains, controllable loads etc.). In that case, either a
decentralized, centralized or distributed supervisory control
needs to be implemented on top of it to decide whether the unit
should operate in droop or some other specific control mode
such as maximum power point tracking (MPPT) [26], [27] or
regulated charging mode [28]. Except for setting operating
modes and managing secondary/tertiary control,
communication technology can also be used to realize
advanced functions such as unit commitment, optimization
procedures or manipulation of internal I-V characteristics by
imposing adaptive mechanisms [14], [28][30].
Along with precise voltage and current regulation, as well
as system level coordination, stable operation of the MG needs
to be ensured in all operating conditions. Tightly regulated
point of load (POL) converters present a challenge from that
point of view since they introduce a negative impedance
characteristic within the bandwidth of their control loops [31],
[32]. This peculiar feature reduces the effective damping and
can even cause instability of the entire system. The
1
refers to the situation where information is
exchanged through DCLs only between units, rather than between units and a
central aggregator.
E
relationship between source and load impedances, often
referred to as the minor loop gain, is an important quantity
which can be used for determining stability [31]. Different
specifications for the minor loop gain have been proposed not
only to ensure stability but also to maintain good system
dynamics after connecting additional elements such as input
filters [31], [33][39]. Modeling of the entire state space is an
alternative option which explicitly takes into account the
complete system but does not provide such a good insight into
dynamics as the impedance based approach. A variety of
passive and active stabilization techniques have been
developed using both methods in order to improve damping of
the system [40][44].
The aim of this article is to provide an overview of control
strategies, stability analysis tools and stabilization techniques
used in DC MGs. It is organized as follows. In Section II,
basic control principles are presented. It is demonstrated how
the overall converter control can be split into local and
coordinated controls. Section III explores in more depth a
number of functionalities within the local control, while
coordinated control is addressed in Section IV. A detailed
analysis of the stability problem is presented in Section V,
where it is shown how a dynamic model of the whole DC MG
system can be conveniently divided into a source and load
subsystems which are characterized by their respective
impedances. It is explained how the relationship of these
impedances defines the stability of the system, and several
prominent impedance specifications and stabilization
principles are reviewed. Concluding remarks and an overview
of future research trends can be found in Section VI.
II. DC MG CONTROL PRINCIPLES
In order to guarantee stable and efficient operation of a DC
MG, effective control strategies should be developed. The
general structure of a DC MG system is shown in Fig. 1. In
general, MG consists of a number of parallel converters that
should work in harmony. Local control functions of these
converters typically cover the following: (I) current, voltage
and droop control for each unit; (II) source dependent
functions, e.g. MPPT for photovoltaic (PV) modules and wind
turbines, or a state-of-charge (SoC) estimation for energy
storage systems (ESSes); (III) decentralized coordination
functions such as local adaptive calculation of VRs, distributed
DC bus signaling (DBS) or power line signaling (PLS). At a
global MG level, a digital communication-based coordinated
control can be implemented to achieve advanced energy
management functions. It can be realized either in a centralized
or a distributed fashion, via central controller (CC) or sparse
communication network, respectively. In case of distributed
control, variables of interest are exchanged only between local
controllers (LCs). Consensus algorithm can then be used to
calculate either the average of all the variable values in
distributed LCs or the exact value of any variable present in a
specific LC. A detailed explanation on how this can be
realized and a review of several consensus applications in DC
MGs can be found in Section IV.C and references therein.
Some of the functionalities that can be accomplished by using
DCLs include secondary/tertiary control, real-time
optimization, unit commitment, and internal operating mode
changing (see Fig. 1 and Section IV for more details) [12].
From the communication perspective, overall control of DC
MGs can be divided into the following three categories:
Decentralized control: DCLs do not exist and power lines
are used as the only channel of communication.
Centralized control: Data from distributed units are
collected in a centralized aggregator, processed and
feedback commands are sent back to them via DCLs.
Distributed control: DCLs exist, but are implemented
between units and coordinated control strategies are
processed locally.
The basic configuration of each of these control structures
is depicted in Fig. 2. A more detailed overview of the
significant features of local and coordinated control strategies
is provided in the following sections.
Fig.1. Systematic control diagram in DC MGs.
(a) (b) (c)
Fig. 2. Operating principles of basic control strategies.
(a) Decentralized control. (b) Centralized control. (c) Distributed control.
III. LOCAL CONTROL IN DC MGS
As previously mentioned, the control framework of a DC
MG consists in general of local and coordinated control levels.
In this section a local control level is discussed in detail. Basic
functions which include current, voltage and droop control are
reviewed. Due to limited space and in an attempt to keep the
scope of the paper as focused as possible, a review of MPPT
and charging algorithms has been omitted here. More details
on charging algorithms for batteries can be found in [45],
while an in-depth analysis of MPPT algorithms has been
presented in a number of references, e.g. in [26], [27].
As a backbone of a DC MG, the interface converters play
an important role in efficient and reliable operation of the
overall system. In order to ensure not only proper local
operation, but also to enable coordinated interconnection
between different modules in a DC MG, flexible local current
and voltage control should be employed and accurate power
sharing among parallel connected converters should be
achieved. The basic local control diagram is shown in Fig. 3,
including local current and voltage controllers, and a droop
control loop.
For local DC current and voltage control systems in DC
MGs, proportional-integral (PI) controllers are commonly used
since they introduce zero steady-state error, can be easily
tuned, and are highly robust [3]. However, use of other types
of controllers such as proportional-derivative (PD), fuzzy and
boundary controllers has also been reported [43], [46][48].
PD controllers can be used to improve the phase margin of the
system, but they do not eliminate steady-state error and also
need to have high frequency poles in order to attenuate high
frequency noise. Hence, rather than appearing in a pure PD
form, the derivative term in a PD controller is usually replaced
by a high-pass digital filter. By combining the beneficial
effects of PI and PD controllers, PID controllers can be
employed. Fuzzy control is designed to emulate a human
stimulus
he/she gets from the environment and his/her own embedded
knowledge. In the engineering world, it can be defined as a
knowledge-based control method that can simultaneously take
advantage of both static and dynamic properties of the system
[49]. For the purpose of local voltage and current regulation
fuzzy controllers can either be used as principal regulators that
process the error signal [46] or in a series with feedback loops.
To ensure fast convergence and extreme robustness, nonlinear
control strategies based on state-dependent switching (e.g.
boundary control in [48]) can be employed. They present
simple implementation, but their detailed performance analysis
can be quite complex. It should be noted that alternative
control methods for DC MGs have recently drawn a lot of
attention in the academic circles. However, their practical
application should be elaborately justified by performing
modeling, analysis, simulation, implementation as well as a
full cost-benefit analysis. For instance, increased production
cost and lead time often prove to be too large of an obstacle
for their deployment.
Droop control is commonly installed on top of inner loops,
primarily for current sharing purposes. Fig. 3 demonstrates that
either output power or output current can be selected as the
feedback signal in droop control [3], [29]. For DC MGs with
power-type load, output power can be used as droop feedback,
as shown in (1). On the other hand, when current signal is
used, as shown in (2), droop coefficient m
c
can be regarded as
a virtual internal resistance. In that case, the implementation
and design of the parallel converter system in a DC MG can be
simplified to some extent as the control law is linear [3]. The
principle of current-based droop control was also extensively
used in distributed power systems (DPSs) for putting in
parallel multiphase converters that supply computer CPUs.
Here, droop control is commonly known as adaptive voltage
positioning (AVP) [50][52]. The calculations of references
for voltage controller in the two aforementioned cases are as
follows:
**
DCi DC p oi
v v m P
(1)
**
DCi DC c oi
v v m i
(2)
where v
DCi
*
is the output of the droop controller, i.e. the
reference value of DC output voltage of converter #i, v
DC
*
is
the rated value of DC voltage; m
p
and m
c
are the droop
coefficients in power- and current-based droop controllers,
while P
oi
and i
oi
are the output power and current of converter
#i, respectively.
The values of droop coefficients have a profound effect on
system stability and current sharing accuracy. In general, the
higher the droop coefficients, the more damped system is and
the better accuracy of current sharing. However, there exists a