Decentralized cooperative control strategy of microsources for stabilizing autonomous vsc based microgrids

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012 1949

Decentralized Cooperative Control Strategy
of Microsources for Stabilizing Autonomous
VSC-Based Microgrids
Poria Hasanpor Divshali, Arash Alimardani, Student Member, IEEE, Seyed Hossein Hosseinian, and
Mehrdad Abedi

Abstract—In designing procedure of a power sharing controller frequency while sharing the active and reactive power. Since
for a voltage source converter (VSC)-based microgrid with no com- most DGs are of relatively low power capacity, maintaining
munication link, three issues should be considered. Firstly, in VSC- the balance of power in autonomous mode has required the
based microgrids, which use droop controller method, the desired
frequency of VSCs is altering regarding the output active power.
participation of all DGs, and this has attracted the attention of
Consequently, the conventional load frequency control techniques several researchers [5]–[8].
are inappropriate since their operation is based on a fixed pre- The DGs in a microgrid, which is operated in islanding mode,
specified desired frequency. Secondly, to prevent circulating cur- should share power between each other in an appropriate ratio to
rent and thermally overstressing, all DGs should participate in ac- prevent circulating current and thermally overstressing or dam-
tive power supply. In addition, since there is no communication aging of components [7]. In the conventional electrical network
link, the steady state value of each micro-source active power is
unknown. Therefore, the conventional fixed active power control with synchronous generator, any alteration in active power bal-
method for DGs is not appropriate. Thirdly, when the microgrid ance causes change in synchronous frequency. Consequently,
loads are increased, the output power of VSCs is increased rapidly; the active power balancing is achieved by regulating the active
however, the output power of each VSC’s primary source could power produced by synchronous generators via the difference of
not change in the same rate to respond. It causes the DC voltage of each generator frequency from the reference frequency. How-
VSCs to decrease, which could affect the appropriate performance
of VSCs. In this paper, a novel control strategy for VSCs and an en-
ever, most DG technologies such as microturbines, fuel cells,
ergy storage system in a VSC-based microgrid without communi- and gas internal combustion engines with permanent magnet
cation link accompanied with a novel hybrid model of VSC-based generator have a convertor to connect to the electrical distri-
DGs, which considers primary source effect, is proposed. bution system [2]. These DG technologies have lower emis-
Index Terms—Autonomous microgrids, distributed generation, sion, and higher efficiency rather than conventional DGs such as
frequency stability, frequency/voltage droop, small signal stability, diesel generator. In these DGs, the output frequency is indepen-
storage system. dent from output power in nature. Therefore, when the micro-
grid does not have any synchronous generator, the conventional
droop method, which measures the error of rotating frequency,
I. INTRODUCTION is not successful.

C ONCERNS about environmental emissions from cen-
tralized power plants, accompanied by the economical
and technical reasons, have increased interest in installation of
In this situation, there are two methods to control voltage
source converter (VSC)-based microgrids. The first con-
trol technique is based on communication links such as the
DGs. However, the penetration of DGs in a power system is master-slave approach [8]. Such techniques can be adapted
limited due to the technical reasons such as stability constraints in systems where DGs are connected to a common bus or
[1]. Therefore, indiscriminate application of individual DGs located in close proximity. This is because it is impractical
can cause as many problems as it may solve [2]. A better way and costly to distribute the dynamic sharing signals, which
to realize the potential of a DG is to take a system approach, are characterized by their high bandwidth in long connection
which views generation and associated loads as a subsystem or distance [9]. Furthermore, reliability issues of the centralized
a microgrid [3]. Microgrids are required to operate in both grid control approach might counteract the positive reliability boosts
connected and islanding (autonomous) modes to increase reli- gained by implementing microgrids [9]. The second control
ability and power quality [4]. In an autonomous microgrid, all technique is based on frequency droop method [6]. In this droop
the DGs are responsible for maintaining the system voltage and method, unlike the conventional droop method, VSCs measure
the output active power and drop the frequency of voltage
based on the measured value. In other words, this method
Manuscript received July 12, 2011; revised October 28, 2011 and January 10, employs the frequency of the network instead of applying a
2012; accepted February 06, 2012. Date of publication April 10, 2012; date of communication link. Although droop control does not ensure
current version October 17, 2012. Paper no. TPWRS-00653-2011.
The authors are with the Department of Electrical Engineering, Amirkabir constant frequency and amplitude of microgrid voltage, the
University of Technology, Tehran, Iran (e-mail: poriahd@gmail.com; arash.al- advantage in avoiding communication-based control makes it
imardani@ieee.org; hosseinian@aut.ac.ir; abedi@aut.ac.ir). a competitive solution for controlling microgrids [10]. As a
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
result, this method is employed for power sharing controller of
Digital Object Identifier 10.1109/TPWRS.2012.2188914 microgrids in papers such as [5] and [6].

0885-8950/$31.00 © 2012 IEEE

1950 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 4, NOVEMBER 2012

VSC-based DGs, which use this frequency droop method, Different studies model the VSC-based DGs with various
have another drawback. When the demand power of the precisions. Some studies on DG modeling consider the primary
microgrid is increased, the output power of VSC increases source without modeling the convertor. Reference [17] models
immediately. On the other hand, primary sources such as the primary source and its controllers completely without
microturbine or fuelcell are limited by insufficient dynamic modeling the convertor, and uses this model to design the DG
performance for load tracking [11]. Consequently, the DC bus controllers. References [13] and [14] used a first-order lag
voltage of VSC could be changed in a manner, which can affect transfer function to model the dynamic response of different
the VSC output voltage. Reference [6] has developed a load DGs output power regardless of the VSC dynamic. The time
sharing method in order to stabilize the operation of microgrid constant of this first-order transfer function is chosen equal
without communication link. However, it assumes that the DC to the biggest time constant of the complete primary source
voltage is constant. Reference [12] indicates that a fast-re- model. Some other studies propose the complete model of
sponse energy storage module must be included in each DG to VSC and primary source together [18]; however, because of
provide a constant DC voltage with different primary sources. the complexity of these models, they are not useful for stability
Installation of energy storage system (ESS) in each DG is very analysis. The others have modeled the VSC and its controller
costly. Hence, some papers focus on installing one ESS for the completely and neglect the dynamic of primary source, or
whole microgrid. References [13] and [14] study the microgrid assume that the DC voltage is fixed, and employ this model
with synchronous generators and a central ESS. These micro- for stability analysis [6], [12]. Reference [6] demonstrates
grids have synchronous generators and use the conventional that when the DC voltage is fixed, the switching process can
frequency control method, which is used in large-scale power be assumed ideal, and it has no effect on stability analysis.
systems. In these studies, the output power of convertor-based Reference [12] shows that each VSC-based DG should have an
DGs is considered constant, and the frequency is applied as the energy storage module in order to keep the DC voltage fixed
input to the control units of synchronous generators and storage and describes the specifications of this storage.
system. However, in a microgrid with no communication link, In this paper, a hybrid model of a VSC-based DG, which con-
the suitable steady state value of micro-sources active power is siders the primary source effect on VSC working, is proposed.
unknown, since no micro-source has adequate information of In this model, the primary source is modeled with first-order
the state of the network. Moreover, no DG is large enough to transfer function as described in [13], the VSC is modeled com-
compensate all the load variations, and all the DGs should par- pletely as described in [6] without the assumption of the fixed
ticipate in active power supply. Hence, considering a constant DC voltage, and the DC voltage is calculated from the differ-
active power for DGs is not appropriate. Reference [15] uses ence between the output power of the VSC and the primary
a single ESS in a microgrid and shows the better frequency source. Consequently, the limitation of VSC’s performance due
control can be achieved by cooperative control strategy of ESS to the DC voltage can be considered. The following subsection
and DGs. However, this cooperative control strategy needs describes the hybrid model of a VSC-based DG.
communication link.
Thus, in this paper, a new cooperative control strategy for A. Proposed Hybrid Model
VSC-based microgrids with no communication link, which con- Fig. 1 shows the block diagram of the complete model of
sist of a single ESS and DGs, is proposed. The proposed method a VSC-based DG and its controller. This model consists of
does not need communication link and guarantees the stability power sharing controller, voltage controller, current controller,
of the VSC-based microgrid with a single ESS. In addition, in switching process, output filter and coupling inductance, DC
order to consider the dynamic performance of primary source bus, and primary source. The dynamic and algebraic equations
and its effect on the VSC work, a new hybrid model for VSC- (DAE) of each component of this model are as follow:
based DGs is proposed. 1) Power Sharing Controller: The power sharing controller
The rest of this paper is organized as follows: microgrid mod- of VSC-based microgrids is based on microgrid frequency and
eling including new proposed method for considering the ef- voltage droop method. This droop method is based on two as-
fect of primary source on VSC performance is described in sumptions. The resistance of line compared to its inductance
Section II. Section III describes a review on the frequency droop could be neglected and the power angle is very small. Conse-
method in VSC-based microgrid and explains the proposed de- quently, the active power is related to the phase angles differ-
centralize cooperative control strategy for autonomous VSC- ences, while the reactive power depends on the voltage magni-
based microgrid. The configuration of test system is described in tudes. As controlling the frequency can dynamically control the
Section IV. The simulation results and discussions are reported phase angle, the active and reactive power can be controlled by
in Section V. Conclusions are stated in Section VI. adjusting the DG output frequency and magnitude of voltage,
respectively. Therefore, the frequency and voltage droop char-
II. MICROGRID MODELING acteristics can be expressed as follows:
Each VSC-based microgrid consists of three major parts in-
cluding the network, loads, and VSC-based DGs. In stability (1)
analysis of VSC-based microgrids, because of the fast dynamic (2)
of VSC and larger R/X ratio of distribution lines than transmis- (3)
sion lines, network and loads should be modeled dynamically.
The dynamic models of network and RL loads are described in where and are the reference frequency and magnitude
several papers such as [6] and [16]. of the DG output voltage, respectively. and are frequency

DIVSHALI et al.: DECENTRALIZED COOPERATIVE CONTROL STRATEGY OF MICROSOURCES 1951

Fig. 1. Block diagram of VSC-based DG and its controller.

and magnitude of the DG voltage in and ; and (12)
are the average output active and reactive power of the DG, (13)
which is generated by a low pass filter with cutoff frequency
(14)
equal to ; and are the gains of the and Q-E droops.
In other words, this method employs the variable frequency where and are the state variable corresponding to current
and magnitude of voltage instead of utilizing a communication PI controller, and other parameters are shown in Fig. 1.
link, and therefore, enables the DG to share the load demand 4) Switching Process: Reference [6] demonstrates that when
without physical communications between them [5], [6]. The the DC voltage is fixed, the switching process can be neglected
differential equations of power sharing controller are as follows and the inverter produces the reference voltage . In
[6]: this condition, the dynamic of primary source has no effect on
VSC output voltage. However, as shown in [12], the fixed DC
(4)
voltage needs the fast-response energy storage in each VSC,
(5) which is very costly.
(6) This paper focuses on the effect of DC voltage alterations
on the performance of VSC working in order to eliminate the
where , , , and are the direct and quadratic com- fast-response energy storage in each VSC-based DG. The output
ponent of output voltage and output current, respectively. voltage of each inverter is related to DC voltage by modulation
and are the frequency of VSC and common microgrid index (MI) as (15). At any moment, the inverter controllers cal-
rotational frame, respectively. is the angle between common culate the MI and then the fire angles of each switch are obtained
microgrid rotational frame and VSC rotational frame. More de- based on this value and switching strategy. The MI has a max-
tails about rotational frame and power sharing controller are de- imum allowable value based on inverter structure and switching
scribed in [6]. strategy, which determines the conditions under which the in-
2) Voltage Controller: The DAEs of voltage controller are verter can work properly. The maximum allowable value of an
as follows [6]: MI in a three-phase inverter with programmed PWM switching
signal is 1.102, which is calculated in subsection B:
(7)
(8)
(9) (15)
(10)
where and are the reference voltage and is the DC
where and are the state variable corresponding to voltage voltage, which is obtained from (24). Consequently, if
PI controller, and other parameters are shown in Fig. 1. , the inverter can produce the reference voltage
3) Current Controller: The DAEs of current controller are . However, if DC voltage reduces drastically so that the
as follows: becomes greater than , the inverter cannot supply the
reference voltage. As a result, should be calculated from (16)
(11) and (17):


(16)

Fig. 2. Primary source model and simple DC voltage controller.
(17)

of the DG can be obtained, previous works in stability analysis
5) Output Filter and Coupling Inductance: The DAE of
assume that the DC voltage is fixed and neglect the effect of
output filter and coupling inductance are as follows [6]:
the primary source model [6], [12]. However, as discussed in
the previous subsections, the effect of the primary source model
(18)
could be vital and should be considered. Therefore, in the pro-
posed hybrid model, which is used for stability analysis, the pri-
(19) mary source is modeled by a first-order lag transfer function as
described in [13] and [14]. This lag transfer function models the
(20) delay of primary source to change its output power, which use
for DC voltage calculation.
(21) Fig. 2 depicts the primary source model with its proposed
controller, which is responsible for regulating the DC voltage.
(22) The input of this model is the active power reference of the pri-
mary source, which is generated by the proposed proportional
(23) differential (PD) controller to fix the DC voltage. The output
power of the primary source is limited by the maximum output
power of it. Equation (25), shown at the bottom of the page, de-
where and are the direct and quadratic components of
scribes the primary source model regarding its controller, where
filter current and other parameters are shown in Fig. 1.
is the time constant of the primary source model and and
6) DC Bus Voltage Model: Each VSC-based DG includes
are the proportional and differential gain of the DC voltage
a DC bus, which connects the primary source to the VSC. This
controller, respectively.
bus is composed of a capacitor as shown in Fig. 1. The capacitor
Generally, the proposed hybrid model considers the primary
voltage changes as follows:
source with the first-order lag transfer function, and the VSC,
on the other hand, is modeled completely. This proposed model
(24)
calculates the DC bus voltage and MI by solving the VSC and
primary source equations, simultaneously. This proposed hy-
where is the capacitor of DC bus, is the time interval of
brid model adds two differential equations to the VSC model,
simulation, is the output power of primary source such
which is presented in [6] to determine MI variations. When MI
as fuelcell, which is obtained from (25), and is the input
crosses the maximum value, the inverter cannot produce the
power of VSC, which is equal to the output power in lossless
reference voltage and reduces its output voltage. This problem
VSCs. Since the MI has a maximum value, the DC voltage of
could lead to a voltage collapse (instability) in microgrid.
VSC has a minimum acceptable margin in order to work prop-
The proposed hybrid model considers the effect of primary
erly.
source without adding complicated primary source model; as
The voltage of DC bus depends on output power of VSC,
a result, it has the capability for stability analysis usage and
output power of primary source, and the capacitor value. As a
ensures that the VSC operates in a feasible operation point as
result, the primary source model affects the DC voltage, and as
two advantages.
has been shown in the previous subsection, if the DC voltage
is reduced from the specified value , the inverter
B. MI Allowable Range
cannot produce the reference voltage. The primary source model
is explained in the next subsection. A three-phase inverter and its typical output voltage with pro-
7) Primary Source Model: Since each primary source has a grammed PWM switching signal are shown in Figs. 3 and 4. The
complicated model from which the output current and voltage amplitude of the th harmonic of the output voltage is given by

(25)


equal to zero to result in the maximum . It is noteworthy
that assigning zero to imposes no further constraints on the
other angles since: .
As all the have negative value, if one could reduce the sum
of them to zero, the best possible set of angles is resulted which
maximizes Z. To do so, the switching angles of each should
be equal. Each thus would become zero and the maximum
MI is reached. By employing such set of switching angles, is
equal to 1 and the maximum MI
is 1.102. The same analysis stands for minimum M ( 1.102),
which is a negative value meaning a shift in the voltage phase.
Fig. 3. Three-phase voltage source inverter configuration.
This argument shows that in order to maintain the output
voltage in a desired value , the DC bus voltage should not
decrease more than .
In this paper, the programmed PWM switching pattern is
chosen because it is one of the most effective mediums in
harmonic elimination, control of fundamental harmonic mag-
nitude, and loss minimization among available PWM schemes
[19]–[26]. Whether the implemented method is programmed
PWM or space vector modulation or any other standard
switching method, the generality of this point is valid that the
DC voltage of the converter should satisfy a limit such as what
was mentioned above.

Fig. 4. Typical output waveform of a PWM inverter. III. DECENTRALIZED COOPERATIVE CONTROL
STRATEGY OF MICROSOURCES

The droop method can share the active and reactive power
between all DGs without communication link. However, this
method has two drawbacks. Eliminating the physical commu-
nication link causes the frequency and amplitude of microgrid
voltage to be constant in different load levels. This makes it im-
(26) possible to use the conventional load/frequency control method,
which is based on constant frequency. The other major draw-
where is the th switching angle and is the number of back of droop method is as follows.
switching angles in a quarter of period as shown in Fig. 4. When the active power demand of microgrid is increased, the
Hence, the MI, which is calculated from the first harmony of output powers of VSCs are increased rapidly and the demand
line to line voltage , is as change is shared between all VSCs based on network parame-
ters. The output power increasing rate of VSCs which are closer
to the location of demand change are more than the others. After
(27) that altering, the droop controllers change the frequency of all
VSCs and after a few seconds, the output powers of VSCs are
shared based on the droop gains. During this time, output power
Mathematical analysis of the following equation indicates of the primary source varies slowly based on its dy-
that the maximum possible value for MI is 1.102: namic performance. Hence, if VSC-based DG does not have an
ESS, the DC voltage is reduced and the MI might reach its limit.
Therefore, the VSC would not work properly.
In this paper, a new cooperative control method, which uses a
single ESS in the whole microgrid and maintains the DC voltage
of all DGs, is proposed. This ESS consists of a battery storage
system or super capacitor system (or a combination), which con-
nects to the microgrid with a VSC. This method includes two
modifications in the present droop technique. The first is related
to the droop controller of a single ESS and the other is related to
(28) the droop controller of DGs. These modifications are described
in the two following subsections. It should be noticed that the
Considering the constraint in (26), it is obvious that all have proposed method does not require any communication link be-
negative value. To maximize Z, first switching angle must be tween generation units.


(32)

where means the absolute value; and are the reliability
coefficients. Equation (31) detects variations in the output
power. This equation calculates the difference between the
output power and the average output power, and compares the
result with the minimum of them. If this difference is bigger
Fig. 5. Frequency droop slope of energy storage system.
than a factor multiplied by the minimum of output power
and the average output power, it means the output power is
A. Control of a Single ESS considerably changed. The factor should be selected so that
all major demand changes are detected in ESS. This value is
The output power of an ESS should be equal to zero in steady
dependent to and , the smaller or the larger leads
state condition and it should be changed rapidly when the de-
to smaller . To determine this value, the microgrid should be
mand of the microgrid is altered in order to stabilize the micro-
simulated in designing process and the and should
grid. In order words, the ESS should work similar to slack bus
be monitored after the critical load increment. In general, when
in the conventional power system but with zero output power
a load increases, initially the output power-increasing rate of
in steady state. For this purpose, the droop controller of the
the closest VSC is more than others. In other words, the farthest
ESS should have a high active gain in steady state. When
VSC to where the load senses the least change. Therefore, the
the demand is changed, the gain should be decreased rapidly
critical load increment is the amount of load increment in the
and then should be increased slowly back to the initial value
farthest bus to the ESS, which leads the MI of one VSC to
as demonstrated in Fig. 5. High gain of the ESS active droop
reach the maximum value, if the ESS does not detect it.
causes the ESS to produce approximate zero active power in
Equation (32) compares the value of this difference with the
steady state condition, and low gain of active droop leads
difference value in the previous step of simulation and checks
the ESS to produce or consume almost all the demand variation
whether the change is new. If the output power is changed and
in dynamic behavior of the microgrid. Consequently, the active
this change is a new change, the value of is updated to . The
droop gain of a single ESS in the proposed method could be ex-
process of selecting is similar to selecting process.
pressed by

(29) B. Control of DGs
The active output power of primary sources changes slowly
where and are the high and low droop gains; is a co- in DGs. Therefore, if the output power of a VSC changes slowly,
efficient, which determines the velocity of increasing the droop too, the DC voltage tolerance is reduced. Therefore, a mecha-
gain from to . The higher , the faster changing of the nism should be implemented to slow the response speed of the
droop, the less ESS energy supplying, and the more decrement VSC. For this purpose, the frequency droop gain of DGs should
in DC voltage of DGs. is the last time that the microgrid’s de- be increased when their output active power changes.
mand is changed and should be determined in the ESS locally References [9] and [28], for better dynamic response of
for decentralized control. VSCs, drop the frequency of VSCs based on the derivation of
When the microgrid’s demand is changed, the output power the output power with respect to time. In this paper, this method
of all DGs and the ESS are changed based on network parame- is used to increase the frequency droop gain when the output
ters. To detect the demand changes of microgrids in ESS locally, power changes. Hence, the DGs droop gain is defined as
a method, which operates based on monitoring output power of
the ESS, is proposed in this paper. For this purpose, first, the (33)
output power of the ESS is compared with its average
in last few seconds. When the output power changed suddenly,
the output power goes away from its average value and based on where is the th DG frequency gain in steady state condi-
this compression, the moment of demand variation is detected. tion and is the coefficient of increasing frequency droop
The average of the output power in last few seconds gain of corresponding DG in relation to absolute of output ac-
is obtained by crossing the output power from first-order lag tive power derivation . Equation (33) results in in-
system with time constant equal to . Therefore, based on creasing the droop gain in dynamic condition. Hence, active
trapezoidal rule [27], is calculated from output power of VSC will change less and DC voltage will be
maintained in its constraint. In other words, the proposed droop
(30) method for DGs helps the single ESS to supply the whole de-
mand variations initially. Afterwards, ESS reduces its output ac-
Based on the proposed method, the last time that the micro- tive power to zero gradually, on the other hand, DGs increase the
grid demand is changed can be detected locally when (31) and rate of their participation in supplying the microgrid demand
(32) are satisfied: slowly. After some seconds, the output of ESS becomes zero,
the storage is ready for next change in demand, and the demand
(31) is shared perfectly between all DGs.


Fig. 6. Configuration of the sample microgrid.

In order to keep DC voltage of all VSC-based DGs fixed, the
ESS should provide almost the whole demand power variations
in the few initial seconds. Consequently, the ESS power rate
should be equal to the largest demand changes in the microgrid.
Otherwise, it is possible that the DC bus of DGs reduces more
and the voltage collapse occurs.

IV. CONFIGURATION OF THE TEST SYSTEM
Fig. 6 presents the configuration of the studied microgrid in
Fig. 7. Output active power of VSC-based DGs in case A.
this paper. This microgrid is the test study of [15] with some
modifications. This system includes two fuelcells and two mi-
croturbines as DGs, a battery storage system as an ESS, a static state condition. The dynamic response of the microgrid is ob-
transfer switch (STS), and four loads. The ESS is placed near tained by applying trapezoidal rule [27] in these state equations.
the point of common coupling (PCC) of low voltage microgrid The details of the obtaining the operation point and dynamic re-
and medium voltage distribution network to be utilized when sponse are described in [30].
the system transits to islanding operation mode. The STS can In this section, three cases are considered. Case A considers
disconnect the microgrid from the distribution network when it the microgrid with an ESS in each DG. In case B, there is no
is necessary. The detailed aspects of the test system are as fol- ESS in the microgrid. Case C simulates the proposed method
lows, and the VSCs parameters are listed in the Appendix. and considers a single ESS at bus 1 (Fig. 6) with no ESS in each
1) Single energy storage system DG. In this case, the single ESS without any communication
a) ESS: 10-kW battery energy storage. link detects the network alteration and produces or absorbs ad-
2) Load (constant impedance): equate active power. In all cases, the simulation is run for 75
a) Load 1:10 kW j6.5 kVAr. s; initially, the microgrid is connected to the distribution net-
b) Load 1:5 kW. work and receives 10 kW j 10 kVAr from it. On , STS
c) Load 1:50 kW j20 kVAr. is opened and the microgrid becomes islanded, and finally, on
d) Load 1:8 kW 8 kVAr. , all loads are increased 10%.
3) DGs:
a) DG1: 10-kVA fuelcell. A. Case A
b) DG2: 70-kVA microturbine.
In this case, the central ESS (in Fig. 6) is not connected; how-
c) DG3: 70-kVA fuelcell
ever, all DGs have an ESS in the DC link. Since the battery
d) DG4: 20-kVA microturbine.
storage system has rapid dynamic ( [14]), all DC
4) Line:
voltages are almost fixed and the MI remains in allowable range
a) Line 1: .
during simulation. The output active power of each DG in this
b) Line 2: .
case is shown in Fig. 7.
c) Line 3: .
As shown in this figure, in , disconnecting from the
d) Line 4: .
utility, DGs output active power are changed rapidly. Among
5) Network: Injects 10 kW j6.5 kVAr.
them, DG1 is closer to PCC, and therefore, its output power-in-
creasing rate is more than the other DGs. After a few seconds,
the active power is shared between all DGs based on their droop
V. SIMULATION STUDY gain, and the system reaches the steady state condition. In
To evaluate the dynamic behavior of the microgrid with and , the loads are increased 10%, and this demand increment
without the proposed cooperative control strategy, the microgrid is shared between all DGs perfectly. The DC voltage and MI of
state space equations are modeled in MATLAB. The state space DGs in case A are shown in Figs. 8 and 9, respectively. These
equations are obtained from VSCs, loads, and network DAE. figures show that the DC voltage of DG1 is changed more than
These equations are solved by Newton method [29] for steady other DGs because its output power is changed more rapidly.


Fig. 8. DC voltage of VSC-based DGs in case A. Fig. 12. Important eigenvalues of the microgrid of case B.

Fig. 9. MI of VSC-based DGs in case A. Fig. 13. Primary source active power of VSC-based DGs in case B.

Fig. 10. Important eigenvalues of the microgrid of case A. Fig. 14. DC voltage of VSC-based DGs in case B.

Fig. 11. Frequency of microgrid in case A. Fig. 15. Modulation index of VSC-based DGs in case B.

However, the MI of all DGs is in the acceptable range and there- ESS, are shown in Fig. 12. This ﬁgure shows that this case has
fore, the microgrid works properly. The important eigenvalues zero eigenvalues and therefore, this microgrid is unstable when
of microgrid in case A demonstrate the small signal stability the demand is changed.
(SSS) of this case as shown in Fig. 10. In order to demonstrate the reason of this instability, it is as-
When the microgrid is in the connected mode, the frequency sumed that the VSC can work perfectly the same as case A. In
of the microgrid is equal to the network frequency. However, this condition, since this case has no ESS and the primary source
in the islanding mode, the frequency changes based on demand dynamic is slow, the DC bus voltage is reduced rapidly and the
and droop gains. The frequency alteration of the microgrid in MI reaches its maximum limit. By this assumption, the primary
this case is shown in Fig. 11. source power, which is obtained from (25), the DC bus voltage,
which is calculated from (24), and the MI, which is obtained
B. Case B from (15), are shown in Figs. 13–15, respectively.
In this case, it is assumed that none of the DGs has ESS, and As stated in (16) and (17), the VSC can produce desired
the single ESS of Fig. 6 is not connected either. Based on the voltage, when the MI is smaller than , which is equal
proposed hybrid VSC-based DG model, which is developed in to 1.102 in this case. When the MI is greater than , the
this paper, the important eigenvalues of this case, which has no output voltage is less than the desired voltage as obtained in


(16) and (17). Fig. 15 demonstrates that the MI is so larger than
1.102, when this microgrid is disconnected from the utility in
, and Fig. 14 shows that the is equal to zero in this
time. Therefore, the output voltage of first VSC is reduced to
zero at this time. Thus, the voltage collapse is occurred and the
microgrid becomes unstable.
Consequently, case B shows that the microgrid with no ESS
cannot work properly. Based on the same reason, previous
works use ESSs in a microgrid. As mentioned above, some
of them use single ESS in microgrid with central controller Fig. 16. Output and average of active power of ESS in case C.
and use the communication link to determine when and how
much the ESS should generates or absorbs the active power.
Others assume all DGs have an ESS and the DC voltage is
fixed. Utilizing a communication link or several ESSs will
impose large cost to microgrid. Therefore, in this paper, a
new method is proposed, which works with a single ESS and
without employing communication link. Case C presents the
simulation results of this proposed method.

C. Case C
Fig. 17. Frequency droop slope of VSC-based DGs and ESS in case C.
In this case, the ESS is connected to bus 1 with the proposed
controller and no DG has separate ESS. The ESS is a battery
storage system, which is modeled by first order lag transfer func-
tion with time constant equal to 0.1 s as described in Section II.
The proposed hybrid model is considered in all DGs and ESS,
and the MI is traced. If the MI reaches its allowable limit, the
VSC output voltage is reduced and the system may become un-
stable. Initially, the system is connected to the distribution net-
work. In , the microgrid is disconnected from the dis-
tribution network. In this time, the output power of all VSCs
is changed. The proposed method based on the conditions de- Fig. 18. Output active power of VSC-based DGs in case C.
scribed in (31) and (32) determines the demand changing (dis-
connecting from network) in (detected with a delay,
which is equal to the sampling time interval), and drop the fre-
quency droop gain suddenly. Also, in , the detec-
tion algorithm of ESS identifies the demand changing and de-
creases the droop gain of ESS. In this case, is set equal to
0.1 and is equal to 0.5. In order to set these values, the crit-
ical load increment is considered (load changes in bus 5, where
is the farthest bus to the ESS). It worth mentioning that several
demand changes are simulated in this case, in order to analyze
the claim of the farthest bus is the critical one and it is observed Fig. 19. Primary source active power of VSC-based DGs in case C.
that the and , which are selected based on critical bus
(bus 5) lead to detect all load changes.
Fig. 16 shows the ESS output power and its average, which zero power in steady state, the steady state output active power
are used for demand change detection . As shown in of DGs in this case is similar to case A (Fig. 7).
this figure, the output power of ESS is increased suddenly and When the VSC output power of the ESS changes slowly, the
decreased slowly in order to provide the opportunity of increase output power of primary source has the opportunity to follow
of the DGs primary source output power and follow the demand it. Hence, the DC voltage will have less variation. The active
variations. power of primary source and the DC voltage of DGs are shown
The frequency droop gain of ESS and DGs, which change in Figs. 19 and 20, respectively.
in time based on the proposed cooperative control strategy are By comparing Fig. 20 with Fig. 14, which shows the DC
shown in Fig. 17. voltage of case B, it is demonstrated that the proposed coop-
The proposed cooperative control strategy causes to increase erative strategy can reduce the DC voltage tolerance of all DGs.
the DGs droop gain when DGs output power changes and de- The MI of all DGs in case C are depicted in Fig. 21.
crease the ESS droop gain when the demand changes as shown Fig. 21 shows that the MI remains in its limits in case C. It
in Fig. 17. This method leads to slow change in the output ac- means that the microgrid with the proposed control strategy can
tive power of VSCs as shown in Fig. 18. Since the ESS produces work by a single storage system without communication link


TABLE I
VSC PARAMETERS

Fig. 20. DC voltage of VSC-based DGs in case C.

Time constant of primary source.

microgrids with no communication link. In such microgrids,
three important issues should be considered:
• During islanding, to maintain power balancing and the
power sharing, the output power of VSCs should be
changed rapidly. However, the dynamic response of pri-
mary source is slow. Hence, the DC bus voltage and the
output voltage of VSC may have fluctuations. To analyze
this situation, the hybrid VSC-based DG model, which
Fig. 21. Modulation index of VSC-based DGs in case C. considers the primary source effect, is proposed in this
paper. In this model, the modulation index is calculated
and the VSC can work properly, if this index remains in
its limitation.
• VSC-based microgrids without synchronous generator and
communication link do not have fixed frequency. Hence,
the conventional load/frequency control method cannot be
employed in these networks. Previous works use the droop
method with an EES in each VSC for load/frequency con-
trol. In this paper, the cooperative control method for ESS
and DGs is proposed which needs only one single ESS in
Fig. 22. Frequency of microgrid in case C. the whole microgrid and no communication link.
• Because of problem of communication link in wide mi-
crogrid, the demand change should be detected in the ESS
locally. The proposed ESS control method detects the de-
mand change in ESS locally and does not need physical
communication link.
The simulation results show the proposed method can guar-
antee the active power balancing in autonomous microgrid and
maintain DC voltage of VSC-based DGs in acceptable range
without an ESS in each of VSC or communication link. In ad-
dition, proposed method satisfies the small signal stability of
Fig. 23. Important eigenvalues of the microgrid of case C. microgrid.

APPENDIX
and maintain its stability. The frequency deviation of the micro- VSC PARAMETERS
grid in this case is shown in Fig. 22. The important eigenvalues The VSC model and controller parameters are as follows:
of microgrid with the proposed cooperative control strategy are , , , , ,
shown in Fig. 23. It is noteworthy that since case C has more , , , ,
VSCs (adding a VSC for a single ESS), this case has a little , , , , , ,
smaller damping ratio than case A [31]. These figures show the , and . Other parameters are listed in
performance of this method to keep frequency regulation and Table I.
SSS in dynamic behavior. Thus, any need to costly ESS in each
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